ournal Am. Ceran. Soc,81655-60(199 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers Yuntian T Zhu, Seth T. Taylor, Michael G. Stout, Darryl P Butt, and Terry C. Lowe Division of Materials Science and Technology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 The oxidation of NicalonTM fibers is a concern, because of the outer surface to the interface where oxidation occurs, and its potential as a reinforcement of high-temperature com ii1)reaction to form a new layer of oxide at the interface osites, whose service conditions involve high-temperature, Obviously, one must consider all three oxidation steps if a oxidizing environments. Two limiting types of oxidatio general relationship for oxidation kinetics is to be found. Deal mechanisms are often used to describe the kinetics: chemi- nd grove did an excellent job in deriving the general oxi- cal-reaction-controlled oxidation. at small oxide thick dation kinetics for a flat plate, which can account for all three nesses, and diffusion-controlled oxidation, at large oxide stages. However, their model is inappropriate for describing the thicknesses. Neither mechanism can satisfactorily describe the intermediate region where the oxidation kinetics are area through which the oxygen diffuses and the total interface controlled jointly by both the chemical reaction rate at the area for the oxidation reaction both remain constant. For a erface and the diffusion of oxygen through the oxide cylindrical geometry, as in the case of fibers, the effective area layer. To describe the entire oxidation process with a gen for oxygen diffusion changes along the diffusion path, and the eral relationship, one must consider all stages of the oxida total interface area for the oxidation reaction decreases as the tion process, namely (i) adsorption of oxygen at the outer oxide thickness increases. Filipuzzi and Naslain' attempted to surface of the oxide, (ii) diffusion of oxygen from the outer derive the oxidation kinetics for cylindrical fibers. However surface toward the interface where oxidation occurs, and they considered only diffusion in their work; thus, applicatio (iii)reaction at the interface to form a new layer of oxide. of their equations is limited to thick oxide layers. a general Previously, a very useful general relationship was derived description of the oxidation kinetics for cylindrical fibers, for the oxidation kinetics for a flat plate, which could ac- which can account for all three stages of oxidation, has not count for all three stages of oxidation. However, that equa been reported to date tion is inadequate to describe the oxidation of cylindrical In this paper, we derive the general oxidation kinetics for fibers, because the effective area for oxygen diffusion NicalonTM fibers. All three stages of the oxidation prod hanges along the diffusion path and the oxidation interfa- incorporated into the derivation. Comparison with expe cial area decreases as the oxide thickness increases for cy tal data of Nicalon TM fibers shows good agreement be betwer lindrical fibers. In this paper, we have derived a general heory and the experimental results kinetic relationship for the oxidation of cylindrical fibers which can account for all stages of oxidation. Comparison IL. Theoretical derivation of the theory with experimental data of Nicalon fibers During the oxidation process, oxygen must diffuse inward to shows good agreem the oxidation interface. where the reaction occurs In the case of NicalonTM (SiC)fibers, CO may also form during the oxi- . Introduction dation reaction 1-16 and must diffuse outward to the outer sur- face. For simplicity, we assume that the oxidation process is YLINDRICAL filaments such as NicalonTM(SiC) fibers(Ni controlled by only one diffusing species. Furthermore, pon Carbon Co., Tokyo, Japan) have been increasingl sume that oxidation proceeds via the inward diffusion used as reinforcements for high-temperature composites. As a gen. Nonetheless, the final oxidation kinetics equation nsequence, extensive studies on their oxidation behavior plicable to the case where oxidation is controlled ve been conducted in recent years. - For small oxide thick nesses, the oxidation kinetics are often approximated as being Nicalon TM fibers contain excessive carbon and will undergo further pyrolysis at elevated temperatures, which causes the oxidation occurs, which yields a linear relationship between the fiber diameter to shrink ,,, At the same time, the fiber oxide thickness and time. As the scale grows, the oxidation diameter should increase when the sic is oxidized to form kinetics become governed primarily by the diffusion of oxygen SiO2, because I mol of SiO2 has a larger volume than I mol of fiber nesses both the chemical reaction and diffusion can have vary with diameter, 8 which will affect the pyrolysis during oxidation. Our experimental results have shown that the total The oxidation process typically has three distinct stages: 10 average diameter change of NicalonTM fibers is only 1.4%after () surface adsorption of oxygen, (ii) diffusion of oxygen from oxidation, which is negligibly small. Therefore, we shall as- sume a constant fiber diameter during the oxidation of NicalonTM fibers for simplicity. As a consequence, the follow- ing oxidation model can only be applied where the fiber diam- J. L. Smialek--contributng editor eter does not change significantly during oxidation Shown in Fig. I is a schematic drawing of a fiber with an oxide layer. The fiber diameter is R, which is assumed to re main constant during the oxidation, and the oxide thickness is Manuscript No. 191280 Received January 14, 1997, approved June 17, 1997 x. The radius of the unoxidized core is u. where Alamos National Laboratory (1) B under the auspices of the U.S. Depariment of Energy, under Contract No. As mentioned in the introduction, oxygen usually must go through three steps during the oxidatio n process
Kinetics of Thermal, Passive Oxidation of Nicalon Fibers Yuntian T. Zhu,* Seth T. Taylor, Michael G. Stout, Darryl P. Butt,* and Terry C. Lowe Division of Materials Science and Technology, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 The oxidation of Nicalon™ fibers is a concern, because of its potential as a reinforcement of high-temperature composites, whose service conditions involve high-temperature, oxidizing environments. Two limiting types of oxidation mechanisms are often used to describe the kinetics: chemical-reaction-controlled oxidation, at small oxide thicknesses, and diffusion-controlled oxidation, at large oxide thicknesses. Neither mechanism can satisfactorily describe the intermediate region where the oxidation kinetics are controlled jointly by both the chemical reaction rate at the interface and the diffusion of oxygen through the oxide layer. To describe the entire oxidation process with a general relationship, one must consider all stages of the oxidation process, namely (i) adsorption of oxygen at the outer surface of the oxide, (ii) diffusion of oxygen from the outer surface toward the interface where oxidation occurs, and (iii) reaction at the interface to form a new layer of oxide. Previously, a very useful general relationship was derived for the oxidation kinetics for a flat plate, which could account for all three stages of oxidation. However, that equation is inadequate to describe the oxidation of cylindrical fibers, because the effective area for oxygen diffusion changes along the diffusion path and the oxidation interfacial area decreases as the oxide thickness increases for cylindrical fibers. In this paper, we have derived a general kinetic relationship for the oxidation of cylindrical fibers, which can account for all stages of oxidation. Comparison of the theory with experimental data of Nicalon™ fibers shows good agreement. I. Introduction CYLINDRICAL filaments such as Nicalon™ (SiC) fibers (Nippon Carbon Co., Tokyo, Japan) have been increasingly used as reinforcements for high-temperature composites. As a consequence, extensive studies on their oxidation behavior have been conducted in recent years.1–9 For small oxide thicknesses, the oxidation kinetics are often approximated as being controlled by chemical-reaction kinetics at the interface where oxidation occurs, which yields a linear relationship between the oxide thickness and time. As the scale grows, the oxidation kinetics become governed primarily by the diffusion of oxygen through the oxide layer toward the oxide/core interface, which yields a parabolic relationship. At intermediate oxide thicknesses, both the chemical reaction and diffusion can have equally significant roles in the oxidation kinetics. The oxidation process typically has three distinct stages:10 (i) surface adsorption of oxygen, (ii) diffusion of oxygen from the outer surface to the interface where oxidation occurs, and (iii) reaction to form a new layer of oxide at the interface. Obviously, one must consider all three oxidation steps if a general relationship for oxidation kinetics is to be found. Deal and Grove10 did an excellent job in deriving the general oxidation kinetics for a flat plate, which can account for all three stages. However, their model is inappropriate for describing the oxidation kinetics of cylindrical fibers. For a flat plate, the total area through which the oxygen diffuses and the total interface area for the oxidation reaction both remain constant. For a cylindrical geometry, as in the case of fibers, the effective area for oxygen diffusion changes along the diffusion path, and the total interface area for the oxidation reaction decreases as the oxide thickness increases. Filipuzzi and Naslain1 attempted to derive the oxidation kinetics for cylindrical fibers. However, they considered only diffusion in their work; thus, application of their equations is limited to thick oxide layers. A general description of the oxidation kinetics for cylindrical fibers, which can account for all three stages of oxidation, has not been reported to date. In this paper, we derive the general oxidation kinetics for Nicalon™ fibers. All three stages of the oxidation process are incorporated into the derivation. Comparison with experimental data of Nicalon™ fibers shows good agreement between theory and the experimental results. II. Theoretical Derivation During the oxidation process, oxygen must diffuse inward to the oxidation interface, where the reaction occurs. In the case of Nicalon™ (SiC) fibers, CO may also form during the oxidation reaction11–16 and must diffuse outward to the outer surface. For simplicity, we assume that the oxidation process is controlled by only one diffusing species. Furthermore, we assume that oxidation proceeds via the inward diffusion of oxygen. Nonetheless, the final oxidation kinetics equation is applicable to the case where oxidation is controlled by the outward diffusion of CO. Nicalon™ fibers contain excessive carbon and will undergo further pyrolysis at elevated temperatures, which causes the fiber diameter to shrink.1,3,11,17 At the same time, the fiber diameter should increase when the SiC is oxidized to form SiO2, because 1 mol of SiO2 has a larger volume than 1 mol of SiC. Furthermore, Nicalon™ fiber has a large diameter variation from filament to filament, and the free-carbon content may vary with diameter,18 which will affect the pyrolysis during oxidation. Our experimental results have shown that the total average diameter change of Nicalon™ fibers is only 1.4% after oxidation, which is negligibly small. Therefore, we shall assume a constant fiber diameter during the oxidation of Nicalon™ fibers for simplicity. As a consequence, the following oxidation model can only be applied where the fiber diameter does not change significantly during oxidation. Shown in Fig. 1 is a schematic drawing of a fiber with an oxide layer. The fiber diameter is R, which is assumed to remain constant during the oxidation, and the oxide thickness is x. The radius of the unoxidized core is u, where u=R−x (1) As mentioned in the introduction, oxygen usually must go through three steps during the oxidation process:10 J. L. Smialek—contributing editor Manuscript No. 191280. Received January 14, 1997; approved June 17, 1997. Supported by the Laboratory Directed Research and Development Office of Los Alamos National Laboratory. This work was performed at Los Alamos National Laboratory under the auspices of the U.S. Department of Energy, under Contract No. W-7405-EN-36. *Member, American Ceramic Society. J. Am. Ceram. Soc., 81 [3] 655–60 (1998) Journal 655
Journal of the American Ceramic Society-Zhu et al. Vol 81. No. 3 d-c dc Equation (7)is a differential equation with the following boundary conditions (at r=R) x-i/ Unoxidized Core atr=R-x) R Q Solving Eq(7)yields dC A d C=AIn r+B where A and B are ants. Substituting Eq.(8) (10)and solving for A yield Fig. 1. Schematic drawing of the cross section of a fiber with Co-C A g.(1)Adsorption of oxygen at the outer layer from the oxI- Substituting Eqs. (9)and(I1)into Eq(4)yields dizing environment. The total oxygen flow per unit time is C-C (2) Diffusion of oxygen from the outer layer to the inter- O2=-2m/D (12) face where oxidation occurs. The total oxygen flow per unit time is denoted as O. (3)Reaction to The total oxygen con new layer of oxide at the interface. Using Eq (2), we set 21=22 and 21=23, which yiel on per unit time is denoted as O3 We assum De d Grove, 10 that the total oxyge per unit time at each of the above-mentioned three steps is the 丌Rh(C*-C0)=-2mD xidation. le Q1=Q2=Q3 2mRIh(C-Co)=2T/(R-x)kCi (13) Assuming that the fiber length, l, is much larger than the fiber radius(ie, />> R), the oxidation from the fiber ends ca Solving Eq(13)for C yields be ignored. The total oxygen flow per unit time from the oxi- dizing environment to the outer fiber surface can be written Ck(1-1),(12104 Or Substituting Eq(14)into Eq(5)yields where h is a gas-phase transport coefficient, Co the oxyger concentration at the outer surface of the oxide. and c* the 2(R一x)C* equilibrium oxygen concentration in the oxide (15) The diffusion flux of oxygen across the oxide layer can be described by Fick's first law: 1-D(R-m(1-)+h(1-R dc(r) Assuming that N is the quantity of oxygen required to form a O2=2TrID (4) unit volume of the oxide layer, the rate of oxide layer growth where r is defined in Fig. 1, C(r) is the oxygen concentration Q within the oxide laver. and d is the diffusion coefficient of oxygen in the oxid Assuming the oxidation is a first-order chemical reaction kC* the total oxygen consumption at the reaction interface is pro- portional to the interface area and the oxygen concentra the interface, C(see Fig. I for definition);1.e 1-b(2-x)n(1-2)+(1-2 O3= 2T(R-x)/kCi (5) Substituting Eq (1)into Eq. (16)yields a differential equation where k is the chemical-reaction rate constant The total oxygen flow per unit time in the oxide layer should remain constant along the diffusion path, which yield (17) 1- Eu In (6) EIn r Substituting Eq(4)into Eq.(6)and simplifying the result with an initial condi u=R( t=0) (1
(1) Adsorption of oxygen at the outer layer from the oxidizing environment. The total oxygen flow per unit time is denoted as Q1. (2) Diffusion of oxygen from the outer layer to the interface where oxidation occurs. The total oxygen flow per unit time is denoted as Q2. (3) Reaction to form a new layer of oxide at the interface. The total oxygen consumption per unit time is denoted as Q3. We assume, as did Deal and Grove,10 that the total oxygen flow per unit time at each of the above-mentioned three steps is the same during oxidation, i.e., Q1 4 Q2 4 Q3 (2) Assuming that the fiber length, l, is much larger than the fiber radius (i.e., l >> R), the oxidation from the fiber ends can be ignored. The total oxygen flow per unit time from the oxidizing environment to the outer fiber surface can be written as10 Q1 4 2pRlh(C* − C0) (3) where h is a gas-phase transport coefficient, C0 the oxygen concentration at the outer surface of the oxide, and C* the equilibrium oxygen concentration in the oxide. The diffusion flux of oxygen across the oxide layer can be described by Fick’s first law: Q2 = 2prlD dC~r! dr (4) where r is defined in Fig. 1, C(r) is the oxygen concentration within the oxide layer, and D is the diffusion coefficient of oxygen in the oxide. Assuming the oxidation is a first-order chemical reaction, the total oxygen consumption at the reaction interface is proportional to the interface area and the oxygen concentration at the interface, Ci (see Fig. 1 for definition); i.e., Q3 4 2p(R−x)lkCi (5) where k is the chemical-reaction rate constant. The total oxygen flow per unit time in the oxide layer should remain constant along the diffusion path, which yields dQ2 dr = 0 (6) Substituting Eq. (4) into Eq. (6) and simplifying the result yields r d2 C dr 2 + dC dr = 0 (7) Equation (7) is a differential equation with the following boundary conditions: C = C0 ~at r = R! C = Ci ~at r = R − x! (8) Solving Eq. (7) yields dC dr = A r (9) and C = A ln r + B (10) where A and B are constants. Substituting Eq. (8) into Eq. (10) and solving for A yields A = − C0 − Ci ln S1 − x RD (11) Substituting Eqs. (9) and (11) into Eq. (4) yields Q2 = −2plD C0 − Ci ln S1 − x RD (12) Using Eq. (2), we set Q1 4 Q2 and Q1 4 Q3, which yields 2pRlh~C* − C0! = −2plD C0 − Ci ln S1 − x RD 2pRlh~C* − C0! = 2pl~R − x!kCi (13) Solving Eq. (13) for Ci yields Ci = C* 1 − k D ~R − x! ln S1 − x RD + k h S1 − x RD (14) Substituting Eq. (14) into Eq. (5) yields Q3 = 2pl~R − x!kC* 1 − k D ~R − x! ln S1 − x RD + k h S1 − x RD (15) Assuming that N is the quantity of oxygen required to form a unit volume of the oxide layer, the rate of oxide layer growth for a cylindrical fiber can be described as dx dt = Q3 2pl~R − x!N = kC* N 1 − k D ~R − x! ln S1 − x RD + k h S1 − x RD (16) Substituting Eq. (1) into Eq. (16) yields a differential equation − du dt = kC* N 1 − Eu ln u + S F R + E ln RDu (17) with an initial condition of u = R ~at t = 0! (18) Fig. 1. Schematic drawing of the cross section of a fiber with an oxide layer. 656 Journal of the American Ceramic Society—Zhu et al. Vol. 81, No. 3
March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers wheree= kd and F= wh are constants under a constant x temperature. Solving Eq. (17)and rearranging the result yield (ER+ 2F)u+2ER(n R-In u)? 2R-x= 2R (30) Rt+M (19) and Substituting the initial condition(Eq(18))into Eq. 19)yields R Substituting Eq(20)into Eq. (19)and rearranging teA. (0) Substituting Eqs. (29)and(30)into Eq(22)and rearranging M=(ER+2F+4)R2 he result yields Gt layer, which means that oxidation is controlled by the rate of where= 4kC N is a constant under a constant temperature chemical reaction Substituting Eq. (1)into Eq. (21)and rearranging the result For the oxidation of a flat plate, the diffusion of oxygen will yields the general relationship for the oxidation kinetics of control the reaction kinetics at a large oxide thickness, which cylindrical fibers yields a parabolic relationship between the oxide thickness x and time t. However, for the oxidation of a cylindrical fiber, the 2F(2-)x+E(2R-x)x+2(R-x2h area of interface at which the oxidation occurs decreases as x ncreases. The shrinking reaction interface will affect the gen (22) eral oxidation kinetics, especially when x approaches the fiber here E, F, and G in Eq (22)are to be determined from fitting radius. When x approaches R (i.e, x-R), the following ap- he experimental data. They are functions of temperature and proximation can be made remain constant for a fixed temperature Many researchers prefer to use an a parameter, which is the (33) fractional reacted volume. instead of oxide thickness. x. to describe oxidation kinetics. 9-1 To compare our results with 2R-xgR their work, we can also write Eq(22)in terms of a, which can be calculated as and (R-x)2ln(1 0 Solving Eq(23)for x yields Substituting Eqs. (33)(35)into Eq.(22) and rearranging the result vield Substituting Eq (24)into Eq (22) yields 2F+ER+4 2FRo+ERa+(1-a)In(1-a) Equation(36)describes a linear rela hip between the oxide +4R[-(1-a)2]=Gt (25) thickness x and time t when x approaches the fiber diameter R, which indicates that the general Equation(22)can be used to describe the oxidation kinetics trolled by the shrinking area of the n kinetics are con- infinity(R-oo), the fiber surface will become essentially flat oxygen diffusion ng area of the and Eq.(22)should approach the oxidation kinetics of a flat plate, as derived by Deal and Grove. 10 This is indeed the case, Ill. Comparison with Experimental Results s demonstrated below. As R approaches infinity, the following and discussions approximation can be made Oxidation experiments were performed on individual (26) NicalonTM fibers(Dow Corning, Midland, MI) that had been separated from a tow. The fibers were heated in a partial ox gen pressure of 0. 14 atm(-0.014 MPa)at a heating rate of 200%C/h to 1200%C. held for 4.8. or 16 h and then furnace cooled to room temperature. A high-resolution scanning elec tron microscopy(SEM)microscope(Model 6300FVX, JEOL, Tokyo, Japan) was used to measure the fiber diameters and the Equation(26)originates from the fact that (R-r)In(I-x/ through a service contract to maintain its accuracy in magni- →-xasR→∞.S and rearranging th ing Eqs. (26)and(27)into Eq ( 22) fication. The measurement was performed directly using the SEM microscope instead of the SEM micrograph print. Before Ex2+4(F+1)x-Gt=0 measurement of the fiber diameter and oxide thickness the sample stage was tilted so that the fiber cross section was Equation(28)is identical to the equation derived by d almost perpendicular to the electron beam, which minimized Grove o for a flat plate when the initial oxide thickness Another special case for Eq.(22)is at the beginning c he possible error caused by tilting the cross section. The fiber diameter and oxide thickness were taken as being the average xidation, when the oxide layer thickness x is approximately of four measurements on each cross section. One cross section zero. The following approximations can be made in this situ- was examined per fiber. Figure 2 shows a typical SEM micro- graph of the cross section of a fiber with an oxide layer
where E = k/D and F = k/h are constants under a constant temperature. Solving Eq. (17) and rearranging the result yields ~ER + 2F!u2 + 2ER~ln R − ln u!u2 + 4uR = S− 4kC* N DRt + M (19) Substituting the initial condition (Eq. (18)) into Eq. (19) yields M = ~ER + 2F + 4!R2 (20) Substituting Eq. (20) into Eq. (19) and rearranging the result yields 2F~R2 − u2 ! + ERSR2 − u2 + 2u2 ln u RD + 4R~R − u! = GRt (21) where G 4 4kC*/N is a constant under a constant temperature. Substituting Eq. (1) into Eq. (21) and rearranging the result yields the general relationship for the oxidation kinetics of cylindrical fibers: 2FS2 − x RDx + EF~2R − x!x + 2~R − x! 2 ln S1 − x RDG + 4x = Gt (22) where E, F, and G in Eq. (22) are to be determined from fitting the experimental data. They are functions of temperature and remain constant for a fixed temperature. Many researchers prefer to use an a parameter, which is the fractional reacted volume, instead of oxide thickness, x, to describe oxidation kinetics.19–21 To compare our results with their work, we can also write Eq. (22) in terms of a, which can be calculated as a = pR2 l − p~R − x! 2 l pR2 l (23) Solving Eq. (23) for x yields x=R[1 − (1 − a) 1/2] (24) Substituting Eq. (24) into Eq. (22) yields 2FRa + ER2 [a + (1 − a) ln (1 − a)] + 4R[1 − (1 − a)1/2] 4 Gt (25) Equation (22) can be used to describe the oxidation kinetics of a cylindrical fiber with a diameter R. When R approaches infinity (R → `), the fiber surface will become essentially flat and Eq. (22) should approach the oxidation kinetics of a flat plate, as derived by Deal and Grove.10 This is indeed the case, as demonstrated below. As R approaches infinity, the following approximation can be made: ~R − x! ln S1 − x RD ≈ −x (26) and x R ≈ 0 (27) Equation (26) originates from the fact that (R − x) ln (1 − x/R) → −x as R → `. Substituting Eqs. (26) and (27) into Eq. (22) and rearranging the result yields Ex2 + 4(F +1)x − Gt 4 0 (28) Equation (28) is identical to the equation derived by Deal and Grove10 for a flat plate when the initial oxide thickness is zero. Another special case for Eq. (22) is at the beginning of the oxidation, when the oxide layer thickness x is approximately zero. The following approximations can be made in this situation: ln S1 − x RD ≈ − x R (29) 2R − x ≈ 2R (30) and R − x ≈ R (31) Substituting Eqs. (29) and (30) into Eq. (22) and rearranging the result yields x = Gt 4~F + 1! (32) Equation (32) indicates a linear relationship between the oxide thickness x and time t under the condition of a very thin oxide layer, which means that oxidation is controlled by the rate of chemical reaction. For the oxidation of a flat plate, the diffusion of oxygen will control the reaction kinetics at a large oxide thickness, which yields a parabolic relationship between the oxide thickness x and time t. However, for the oxidation of a cylindrical fiber, the area of interface at which the oxidation occurs decreases as x increases. The shrinking reaction interface will affect the general oxidation kinetics, especially when x approaches the fiber radius. When x approaches R (i.e., x → R), the following approximation can be made: 2 − x R ≈ 1 (33) 2R − x ≈ R (34) and ~R − x! 2 ln S1 − x RD ≈ 0 (35) Substituting Eqs. (33)–(35) into Eq. (22) and rearranging the result yields x = Gt 2F + ER + 4 (36) Equation (36) describes a linear relationship between the oxide thickness x and time t when x approaches the fiber diameter R, which indicates that the general oxidation kinetics are controlled by the shrinking area of the reaction interface, instead of oxygen diffusion. III. Comparison with Experimental Results and Discussions Oxidation experiments were performed on individual Nicalon™ fibers (Dow Corning, Midland, MI) that had been separated from a tow. The fibers were heated in a partial oxygen pressure of 0.14 atm (∼0.014 MPa) at a heating rate of 200°C/h to 1200°C, held for 4, 8, or 16 h, and then furnace cooled to room temperature. A high-resolution scanning electron microscopy (SEM) microscope (Model 6300FVX, JEOL, Tokyo, Japan) was used to measure the fiber diameters and the oxide thickness. The SEM microscope was calibrated regularly through a service contract to maintain its accuracy in magnification. The measurement was performed directly using the SEM microscope instead of the SEM micrograph print. Before measurement of the fiber diameter and oxide thickness, the sample stage was tilted so that the fiber cross section was almost perpendicular to the electron beam, which minimized the possible error caused by tilting the cross section. The fiber diameter and oxide thickness were taken as being the average of four measurements on each cross section. One cross section was examined per fiber. Figure 2 shows a typical SEM micrograph of the cross section of a fiber with an oxide layer. March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers 657
Journal of the American Ceramic Society-Zhu et al. Vol 81. No. 3 Huger et al. reported results of a thermogravimetric analysis TGA)of Nicalon TM fibers in air in the range of 700-1200oC They also converted the mass gain that was measured using TGa to an oxide thickness as a function of oxidation time The experimen ata are con pared with the present model (Eq. (22)and the Deal and Grove(D&G) model in Fig. 4 Both models agree well with experimental data for oxidation temperatures in the range of 7000-1000.C. As will be dis- cussed later(see Fig. 6), the present model and the Deal and Grove model show a pronounced difference only at the later stage of oxidation. Therefore. we cannot determine which model agrees better with the experimental data shown in Fig. 4 because these data are only from the of oxidation For oxidation temperatures of 1 100 and 1200C and times >30 h. the actual oxide thickness decreases below that which is predicted by both models; this is because these models are not valid anymore for temperatures >1100oC, because of the rea- son discussed below 2·kmm Several factors may affect the accuracy of Eq.(22), when compared with the experimental data of the NicalonTM fibers an oxide layer; the fiber has been treated at 1200oC for 8 h in an sion of co, which is a reaction product at the oxidaton. Fig. 2. Typical SEM micrograph of the cross section of a fiber with First, the present theory does not consider the outward diffu- oxygen partial pressure of 0. 14 atm (-0.014 MPa) face when SiC reacts with O2. In addition, further pyrolytic reaction may occur in the core of Nicalon TM fibers SiC121O04(3)0.9058(s)+0.095s0(g)+0.305C0g) The present theory(Eq(22)) is compared with the experi- lental data in Fig. 3. Because initial oxidation is inevitabl The outward diffusion of the pyrolysis products-gaseous Sic an initial oxide thickness of 0.08 um(which would have re- and Co-will exaggerate the situation. As the oxide layer be- uired -30 min to form if the fibers would have been intro comes thicker, the outward diffusion of CO and Sio may be- duced directly into a furnace preheated to 1200C)is assumed come a limiting factor and slow the oxidation-reaction kinetics to be present and is used in the calculation of Eq(22). Figure If the oxide thickness is large enough, gas bubbles may form in shows that the measured oxide thicknesses are in statistical he oxide layer, as shown in Fig. 5, which renders the present agreement with the values calculated using Eq(22) for oxida ion durations of 4 and 8 h but is smaller than the thickness that The scatter of the fiber diameter may also affect the accuracy is calculated for an oxidation duration of 16 h. The large scatter of Eq (22). An average fiber diameter of 16 um has been used in the data can be attributed to the fact that Nicalon M fiber in the calculations shown in Figs. 3 and 4, whereas the actual have a large diameter variation(from 8 um to 22 um), and ter scatters over a range of 8-22 um. 8 The initial compositions may vary from fiber to fiber although they are during the heating of the fibers to the designated from the same tow. Note that the error bars in Fig. 3 give the ror when using Eq actual range of data scatter zzi and Naslain' and Costello et aL. 22 also attributed Average thicknes Time Fig 3. Compa of the present theory(Eq(22)) with experimental data Parameters for the calculation using Eq (22)are E= 225, F=0.025. and G= 4.5 verage fiber radius R of 8 um has been the calculation
The present theory (Eq. (22)) is compared with the experimental data in Fig. 3. Because initial oxidation is inevitable during the heating of fibers from room temperature to 1200°C, an initial oxide thickness of 0.08 mm (which would have required ∼30 min to form if the fibers would have been introduced directly into a furnace preheated to 1200°C) is assumed to be present and is used in the calculation of Eq. (22). Figure 3 shows that the measured oxide thicknesses are in statistical agreement with the values calculated using Eq. (22) for oxidation durations of 4 and 8 h but is smaller than the thickness that is calculated for an oxidation duration of 16 h. The large scatter in the data can be attributed to the fact that Nicalon™ fibers have a large diameter variation (from 8 mm to 22 mm),18 and compositions may vary from fiber to fiber although they are from the same tow. Note that the error bars in Fig. 3 give the actual range of data scatter. Huger et al.8 reported results of a thermogravimetric analysis (TGA) of Nicalon™ fibers in air in the range of 700°–1200°C. They also converted the mass gain that was measured using TGA to an oxide thickness as a function of oxidation time. Their experimental data are compared with the present model (Eq. (22)) and the Deal and Grove (D&G) model in Fig. 4. Both models agree well with experimental data for oxidation temperatures in the range of 700°–1000°C. As will be discussed later (see Fig. 6), the present model and the Deal and Grove model show a pronounced difference only at the later stage of oxidation. Therefore, we cannot determine which model agrees better with the experimental data shown in Fig. 4, because these data are only from the early stage of oxidation. For oxidation temperatures of 1100° and 1200°C and times >30 h, the actual oxide thickness decreases below that which is predicted by both models; this is because these models are not valid anymore for temperatures >1100°C, because of the reason discussed below. Several factors may affect the accuracy of Eq. (22), when compared with the experimental data of the Nicalon™ fibers. First, the present theory does not consider the outward diffusion of CO, which is a reaction product at the oxidation interface when SiC reacts with O2. In addition, further pyrolytic reaction may occur in the core of Nicalon™ fibers:9 SiC1.21O0.40(s) → ← 0.905SiC(s) + 0.095SiO(g) + 0.305CO(g) (37) The outward diffusion of the pyrolysis products—gaseous SiO and CO—will exaggerate the situation. As the oxide layer becomes thicker, the outward diffusion of CO and SiO may become a limiting factor and slow the oxidation-reaction kinetics. If the oxide thickness is large enough, gas bubbles may form in the oxide layer, as shown in Fig. 5, which renders the present theory totally inapplicable. The scatter of the fiber diameter may also affect the accuracy of Eq. (22). An average fiber diameter of 16 mm has been used in the calculations shown in Figs. 3 and 4, whereas the actual fiber diameter scatters over a range of 8–22 mm.18 The initial oxidation during the heating of the fibers to the designated temperature can be another source of error when using Eq. (22). Filipuzzi and Naslain1 and Costello et al.22 also attributed Fig. 2. Typical SEM micrograph of the cross section of a fiber with an oxide layer; the fiber has been treated at 1200°C for 8 h in an oxygen partial pressure of 0.14 atm (∼0.014 MPa). Fig. 3. Comparison of the present theory (Eq. (22)) with experimental data. Parameters for the calculation using Eq. (22) are E 4 225, F 4 0.025, and G 4 4.5; an average fiber radius R of 8 mm has been used in the calculation. 658 Journal of the American Ceramic Society—Zhu et al. Vol. 81, No. 3
March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers Time (hour) Fig 4. Comparison of the present model(Eq(22))and the Deal and Grove(D&G)me the experimental data of Huger fiber radius R of 8 um was used in the calculation. Parameters for Eq(22)are as follows °C:E=50,F=0.8,andG= E=710,F=001,andG=113, and for120cE=110=00andG=380 E=430,F=0.05,andG= the slowing of the oxidation kinetics to the crystallization of the To fully examine the oxidation kinetics of cylindrical fibers orphous oxide film to cristobalite, which has been detected we assume that a fiber with a diameter of 16 um is oxidized at temperatures as low as 1 100C. The diffusion of oxygen with the entire process obeying Eqs. (22)and(25). Assuming through the cristobalite is more difficult than through an amor- values of E 500, F= 0. 1, and G 2, the oxidation kinetics phous SiO2 layer, which will slow the oxidation kinetics. The are calculated as shown in Fig. 6. For comparison, the oxida- ormation of cristobalite renders both the present model and the tion kinetics of a flat plate predicted by the theory of Deal and Deal and Grove model invalid for temperatures >1100oC Note Gro that the present model is in good agreement with the experi mental data at s1000%C. where the cristobalite does not form This observation indicates that the formation of cristobalite at 1 100 and 1200C could be one of the reasons for the discrep. cy between the present model and the experimental data shown in Fig. 4 for the oxidation of Nicalon m fibers at the two temperatures To evaluate the present theory more rigorously, experimen 5 tioned complications. One such experiment could be the oxi- 8 4 need to be performed on fibers that do not have the foremen dation of pure silicon fiber at a temperature <1100C. Despite these complications, however, the present theory agrees quite well with the experimental data Present thoery for fiber(Eq. 22) Deal et al for fate plate (Eq, 38 sE39cL 0500010000150002000025000 Fig. 6. Comparison of the present theory(Eqs. (22)and(25)for the oxidation of cylindrical fibers with the theory of Deal and Grovel (Eqs. (38)and(39)for the oxidation of a flat plate. Equations(22)and Fig. 5. Bubbles form in the oxide layer of a fiber treated at 1200 C(38)use the oxide thickness, whereas Eqs. (25)and(39)use the for 32 h in ygen partial pressure of 0. 14 atm (-0.014 MP fractional reacted volume to describe the oxidation kinetic
the slowing of the oxidation kinetics to the crystallization of the amorphous oxide film to cristobalite, which has been detected at temperatures as low as 1100°C.1 The diffusion of oxygen through the cristobalite is more difficult than through an amorphous SiO2 layer, which will slow the oxidation kinetics. The formation of cristobalite renders both the present model and the Deal and Grove model invalid for temperatures >1100°C. Note that the present model is in good agreement with the experimental data at #1000°C, where the cristobalite does not form. This observation indicates that the formation of cristobalite at 1100° and 1200°C could be one of the reasons for the discrepancy between the present model and the experimental data shown in Fig. 4 for the oxidation of Nicalon™ fibers at these two temperatures. To evaluate the present theory more rigorously, experiments need to be performed on fibers that do not have the aforementioned complications. One such experiment could be the oxidation of pure silicon fiber at a temperature <1100°C. Despite these complications, however, the present theory agrees quite well with the experimental data. To fully examine the oxidation kinetics of cylindrical fibers, we assume that a fiber with a diameter of 16 mm is oxidized with the entire process obeying Eqs. (22) and (25). Assuming values of E 4 500, F 4 0.1, and G 4 2, the oxidation kinetics are calculated as shown in Fig. 6. For comparison, the oxidation kinetics of a flat plate predicted by the theory of Deal and Grove10 Fig. 4. Comparison of the present model (Eq. (22)) and the Deal and Grove (D&G) model with the experimental data of Huger et al; 8 an average fiber radius R of 8 mm was used in the calculation. Parameters for Eq. (22) are as follows: for 700°C: E 4 50, F 4 0.8, and G 4 0.085; for 800°C: E 4 100, F 4 0.4, and G 4 0.31; for 900°C: E 4 230, F 4 0.1, and G 4 0.95; for 1000°C: E 4 430, F 4 0.05, and G 4 3.0; for 1100°C: E 4 710, F 4 0.01, and G 4 11.3; and for 1200°C: E 4 1100, F 4 0.001, and G 4 38.0. Fig. 5. Bubbles form in the oxide layer of a fiber treated at 1200°C for 32 h in an oxygen partial pressure of 0.14 atm (∼0.014 MPa). Fig. 6. Comparison of the present theory (Eqs. (22) and (25)) for the oxidation of cylindrical fibers with the theory of Deal and Grove10 (Eqs. (38) and (39)) for the oxidation of a flat plate. Equations (22) and (38) use the oxide thickness, whereas Eqs. (25) and (39) use the fractional reacted volume, to describe the oxidation kinetics. March 1998 Kinetics of Thermal, Passive Oxidation of Nicalon Fibers 659
Journal of the American Ceramic Society-Zhu et al. Vol 81. No. 3 x+ Ax= Br (38) 4C. vahlas and F. Laanani, " Thermodynamic Study of the Thermal Degra C-Based Fibers: Intluence of sic Grain Size. "' Mater. Sci. Lent 14,1558-61(1995) SPh. Schreck, C. Vix-Guterl, P. Ehrburger, and J. Lahaye, ""Reactivity R2[2-a-2(1-a)12]+AR[1-(1-a)2]=Bt(39) and Molecular Structure of Silicon Carbide Fibers Derived from bosilanes, Part I. Thermal Behavior and Reactivity, J. Mater. Sci., 27 (where A=0. 16774 and B=0.002376 are obtained by fitting (25 Wano F y by x-Ray Photoelectron Spectroscopy, Eq (38)to the curve calculated using Eq (22)for a time range Carbide: Whiskers stud into Eq.(38))are also plotted in Fig. 6. Equation(38)predicts Maniette and A. Oberlin, "TEM Characterization of Some Crude diffusion-controlled oxidation process when the oxide thick ir Heat-Treated SiC Nicalon Fibers, J. Mater. Sci. 24. 3361-70 ess x is large. The present theory(Eqs. (22)and(25)agrees M. Huger, S. Bouchard and C. Gault, ""Oxidation of Nicalon SiC Fibers well with the equation of Deal and Grove o(Eqs. (38)and(39) J Mater. Sci.' Let, 12, 414-16(1993) when x is <2.5 um, and their difference becomes larger as x "T. Shimoo, H. Chen, and K. Okamura,"High-Temperature Stability of increases. The cylindrical geometry of a fiber results in a Nicalon under Ar or O2 Atmosphere, " J Mater. Sct, 29, 456-63(1994) higher oxidation rate than the flat geometry of a plate, which IoB E. Deal and A S. Grove, "General Relationship for the Thermal Oxi- indicates that the effect of the shrinking reaction interface of a dation of Silicon, J. AppL. Phys., 36, 3770-78(1965) IC. Vahlas, P. Bocabois, and C. Bernard, "" Thermal Degradation Mecha cylindrical fiber becomes stronger as the unreacted fiber core nisms of Nicalon Fiber: A Thermodynamic Simulation, "J.Mater. Sci., 29 becomes smaller, so that the reaction kinetics are jointly con- 5839-46(I9 trolled by oxygen diffusion and the shrinking reaction interface 12K. L. Luthra, ""Some New Perspective on Oxidation of Silicon Carbide and Pultz and w. Hertl,"SiO, SiC Re IV. Conclusions tures, Part 1. Kinetics and Mechanism, Trans. Faraday Soc., 62, 2499-504 A general kinetic relationship for the oxidation of cylindrical A. Gulbransen and S.A. Jansson, " The High-Temperature Oxidation, fibers has been derived which can take into account both ox Reduction, and Volatilization Reaction of Silicon and Silicon Carbide, Oxid MeL,4,18l-201(1972) en diffusion and reaction kinetics at the outer fiber surface and K.E. Spear, and R. E. Tressler,""Passive- at the oxide/unoxidized- core interface. Comparison with the de between8o0°Cand experimental data shows good agreement between theory and 2897-911(1996) the observed oxidation kinetics of Nicalon TM fibers at tempera of 7000-1000oC. A cylindrical fiber has an 17RE Adv. Ceran. Mater, 2, 137-41(1987) oxidation rate that is similar to that of a flat plate when the 7R. Bodet, J. Lamon, N. Jia, and R. E. Tressler, " Microstructural Stabili of Si-C-O(Nicalon)F Monoxide and Argon oxide thickness is small: however, the oxidation rate is higher Am. Ceram.Soc,79,2673-86(1996 when the oxide thickness is large. which indicates that the S T. Taylor, Y. T. Zhu, w.R. Blumenthal, M. G. Stout, D. P. Butt, and reaction kinetics are jointly controlled by oxygen diffusion and the shrinking reaction interface Tanaka, and J. Sestak, On the Fractional Conversion a in Kinetic Description of Solid-State Reactions, "J. Therm. AnaL., 38, 2553-57 Referer R. Frade and M. Cable, "Reexamination of the Basic Theoretical Model for the Kinetics of Solid-State Reactions. Am. Ceram. Soc. 75. 1949-57 Fibers": pp 35-46 in Adranced Structural Inorganic Composites. Edited by P. Vincenzini. Elsevier Science Publishers B V, New York, I ea and H. tan Conventional Kinetic Analysis of the Thermo- CT.Ma, N E ec t, E. MeCi.lum, P.R. oenieman. h 1985, dation ot gav.ms 25-26 199 h. Thermal Decomposition of a solid, Thermochem. 223. A. Costello and R.E. Tressler. "Oxidation Kinetics of Silicon Carbide Katz, and H A. Lipsitt,"Thermal Stability of SiC Fibers(Nicalon"), Crystals and Ceramics; Part I. Experimental Studies, J. Am. Ceram. Marer.Sc,19,1191-201(1984). 674-81(1986
x2 + Ax = Bt (38) and R2 [2 − a − 2(1 − a) 1/2] + AR[1 − (1 − a) 1/2] 4 Bt (39) (where A 4 0.16774 and B 4 0.002376 are obtained by fitting Eq. (38) to the curve calculated using Eq. (22) for a time range of 0–2000 h, and Eq. (39) is obtained by substituting Eq. (24) into Eq. (38)) are also plotted in Fig. 6. Equation (38) predicts a diffusion-controlled oxidation process when the oxide thickness x is large. The present theory (Eqs. (22) and (25)) agrees well with the equation of Deal and Grove10 (Eqs. (38) and (39)) when x is <2.5 mm, and their difference becomes larger as x increases. The cylindrical geometry of a fiber results in a higher oxidation rate than the flat geometry of a plate, which indicates that the effect of the shrinking reaction interface of a cylindrical fiber becomes stronger as the unreacted fiber core becomes smaller, so that the reaction kinetics are jointly controlled by oxygen diffusion and the shrinking reaction interface. IV. Conclusions A general kinetic relationship for the oxidation of cylindrical fibers has been derived, which can take into account both oxygen diffusion and reaction kinetics at the outer fiber surface and at the oxide/unoxidized-core interface. Comparison with the experimental data shows good agreement between theory and the observed oxidation kinetics of Nicalon™ fibers at temperatures in the range of 700°–1000°C. A cylindrical fiber has an oxidation rate that is similar to that of a flat plate when the oxide thickness is small; however, the oxidation rate is higher when the oxide thickness is large, which indicates that the reaction kinetics are jointly controlled by oxygen diffusion and the shrinking reaction interface. References 1 L. Filipuzzi and R. Naslain, ‘‘Oxidation Kinetics of SiC-Based Ceramic Fibers’’; pp. 35–46 in Advanced Structural Inorganic Composites. Edited by P. Vincenzini. Elsevier Science Publishers B.V., New York, 1991. 2 T. J. Clark, R. M. Arons, and J. B. Stamatoff, ‘‘Thermal Degradation of Nicalon™ SiC Fibers,’’ Ceram. Eng. Sci. Proc., 6, 576–88 (1985). 3 T. Mah, N. L. Hecht, D. E. McCullum, J. R. Hoenigman, H. M. Kim, A. P. Katz, and H. A. Lipsitt, ‘‘Thermal Stability of SiC Fibers (Nicalont),’’ J. Mater. Sci., 19, 1191–201 (1984). 4 C. Vahlas and F. Laanani, ‘‘Thermodynamic Study of the Thermal Degradation of SiC-Based Fibers: Influence of SiC Grain Size,’’ J. Mater. Sci. Lett., 14, 1558–61 (1995). 5 Ph. Schreck, C. Vix-Guterl, P. Ehrburger, and J. Lahaye, ‘‘Reactivity and Molecular Structure of Silicon Carbide Fibers Derived from Polycarbosilanes, Part I. Thermal Behavior and Reactivity,’’ J. Mater. Sci., 27, 4237–42 (1992). 6 P. S. Wang, S. M. Hsu, and T. N. Wittberg, ‘‘Oxidation Kinetics of Silicon Carbide Whiskers Studied by X-Ray Photoelectron Spectroscopy,’’ J. Mater. Sci., 26, 1655 (1991). 7 Y. Maniette and A. Oberlin, ‘‘TEM Characterization of Some Crude or Air Heat-Treated SiC Nicalon Fibers,’’ J. Mater. Sci., 24, 3361–70 (1989). 8 M. Huger, S. Souchard, and C. Gault, ‘‘Oxidation of Nicalon SiC Fibers,’’ J. Mater. Sci. Lett., 12, 414–16 (1993). 9 T. Shimoo, H. Chen, and K. Okamura, ‘‘High-Temperature Stability of Nicalon under Ar or O2 Atmosphere,’’ J. Mater. Sci., 29, 456–63 (1994). 10B. E. Deal and A. S. Grove, ‘‘General Relationship for the Thermal Oxidation of Silicon,’’ J. Appl. Phys., 36, 3770–78 (1965). 11C. Vahlas, P. Bocabois, and C. Bernard, ‘‘Thermal Degradation Mechanisms of Nicalon Fiber: A Thermodynamic Simulation,’’ J. Mater. Sci., 29, 5839–46 (1994). 12K. L. Luthra, ‘‘Some New Perspective on Oxidation of Silicon Carbide and Silicon Nitride,’’ J. Am. Ceram. Soc., 74, 1095–103 (1991). 13W. W. Pultz and W. Hertl, ‘‘SiO2 + SiC Reaction at Elevated Temperatures, Part 1. Kinetics and Mechanism,’’ Trans. Faraday Soc., 62, 2499–504 (1966). 14E. A. Gulbransen and S. A. Jansson, ‘‘The High-Temperature Oxidation, Reduction, and Volatilization Reaction of Silicon and Silicon Carbide,’’ Oxid. Met., 4, 181–201 (1972). 15C. E. Ramberg, G. Cruciani, K. E. Spear, and R. E. Tressler, ‘‘PassiveOxidation Kinetics of High-Purity Silicon Carbide between 800°C and 1100°C,’’ J. Am. Ceram. Soc., 79, 2897–911 (1996). 16G. H. Schiroky, ‘‘Oxidation Behavior of Chemically Vapor-Deposited Silicon Carbide,’’ Adv. Ceram. Mater., 2, 137–41 (1987). 17R. Bodet, J. Lamon, N. Jia, and R. E. Tressler, ‘‘Microstructural Stability and Creep Behavior of Si-C-O (Nicalon) Fibers in Carbon Monoxide and Argon Environments,’’ J. Am. Ceram. Soc., 79, 2673–86 (1996). 18S. T. Taylor, Y. T. Zhu, W. R. Blumenthal, M. G. Stout, D. P. Butt, and T. C. Lowe, ‘‘Characterization of Nicalon Fibers with Varying Diameters. Part I: Strength and Fracture Studies,’’ J. Mater. Sci., in press. 19N. Koga, H. Tanaka, and J. Sestak, ‘‘On the Fractional Conversion a in the Kinetic Description of Solid-State Reactions,’’ J. Therm. Anal., 38, 2553–57 (1992). 20J. R. Frade and M. Cable, ‘‘Reexamination of the Basic Theoretical Model for the Kinetics of Solid-State Reactions,’’ J. Am. Ceram. Soc., 75, 1949–57 (1992). 21N. Koga and H. Tanaka, ‘‘Conventional Kinetic Analysis of the Thermogravimetric Curves for the Thermal Decomposition of a Solid,’’ Thermochem. Acta, 183, 125–26 (1991). 22J. A. Costello and R. E. Tressler, ‘‘Oxidation Kinetics of Silicon Carbide Crystals and Ceramics: Part I. Experimental Studies,’’ J. Am. Ceram. Soc., 69, 674–81 (1986). h 660 Journal of the American Ceramic Society—Zhu et al. Vol. 81, No. 3
