Table Ill. Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite Reacted at 1200%C Composition(wt%) Stabilized celsian Fluorokinoshitalite lon species Bulk Interface erface 13.52±0.10 25.42±0.10 20.78±0.58 27.29 0.46 5.13±0.10 1.31±0.10 1.59±0.16 721±0.10 5.32±0.10 0.57±0.1 十一十 ±0.10 1442±0.18 0.10 ±0. 21.45±0.10 7.64±0.10 13.11±0.13 1102±0.20 33.27±0.71 32.11±0. 5.63±0.12 5.25±0.08 Total 10091±0.10 100.97±0.10 9973±0.0 100.23±0.55 Table IV. Stoichiometry of Bulk and Interfacial 3(a), the concentrations of these two tetrahedral cations vary with Compositions of K-Sr Stabilized Celsian and the distance s away from the interface(which is E=0).Thus, one Fluorokinoshitalite reacted at 1200oC realizes that D'eld Dmca(where the superscripts are associated with feldspar and mica phases, respectively ) Furthermore, neither Ba,ksSr.MguKAlSi)Os (Ba,ksSreMgAAl SHOnoFs tend nor Dmica has a unique value; instead, each is a function of distance, time, and temperature. The diffusion profile, of Si",for example, in each phase is characterized by the error-function form a 0.31 that is the solution to Ficks second law. In this problem, however the continuity condition () must be active everywhere 0.04 2.85 including at the interface. The significant consequence of this fact defg 2.75 is that the specific two-phase(local) equilibrium established at the 2.01 2.41 nterface is a function of the initial compositions of the reactants 1.38 and the relative values of Feld and Dmica at E=0. Thus, writing Eq (9)specifically for the Si t flux at the interface(using the eq dXs样+ energy of reaction is dissipated by the motions of other species(an (12) application of the"steady-state approximation"frequently used in species would disallow the accumulation of an electrical approach has been fully articulated by Jostand evertheless, the motions of Al and Si cations are coupled for this mica-feldspar interdiffusion problem, the result is by a molar -flux constraint, which is the second continuity condi- substitution of AP+and Si cations between feldspar and me tion. This constraint means that there must be a one-to (13) that is, maintenance of the mica and feldspar structures requires that the tetrahedral cation fluxes be coupled. Mathematically, this where the subscript"int" denotes a value at the interface and the constraint is articulated as subscript "bulk" denotes a value associated with a reactant. In application to the diffusion data presented in Tables I and Il, for JAI the reaction of stabilized celsian with fluorokinoshitalite at One can substitute the Fick-Einstein flux equations for the Al+ 1300 C, Xfel int =0.169, xs 4, bulk=0.185, xs int=0.108,and and Si+ species from Eqs. (6)into Eq (9)and, realizing that the 0. 101; these values, when placed in Eq.(13), giv lectrical potential is mitigated by the rapid motion of the alkali A simple comparison by inspection of the and alkaline-earth species, solve for the binary chemical (inter ldif- gradients of Si composition at 5=0 in Fig 3(a)(see Eq(12)) of the simple molar-flu supports a relative difference of this magnitude. Application of Eq onstraint, results in a simple Nernst-Planck form, i.e These differences in interdiffusion coefficients for the tetrahedral DAB+D species are consistent with the limited database for similar inter- D=xu-Dau+Xa D s diffusion reactions in metamorphic rock assemblages where X is the mole fraction, The above-given argument, given the US Summary and Comment simplifies to one that can be analyzed using the typically applied form of Ficks first law, that is, for each phase The results of this investigation illustrate two different aspec of the petromimetic approach to the successful engineering of functional fluoromica-interphase/silicate-matrix interfaces for ap- (I1) plication in an alumina-fiber ceramic composite. The first aspect demonstrates the necessity of chemical buffering-i.e, the need with a similar expression for jAi+ for a polyphase matrix that includes both spinel and forsterite--to Because of the differences in the structures of the two phases in stabilize the fluoromica interphase structurally against degradation the reaction couple, the intrinsic diffusion coefficients for the Al due to alumina- or silica-excess feldspar-matrix stoichiometries. The and Si*+ cations will be different in each phase. Furthermore, as is MgO additions decrease the activity of the excess species by com- readily apparent from the diffusion profiles presented in, e.g., Fig. bining to form either spinel or forsterite. Thus, the thermodynamicenergy of reaction is dissipated by the motions of other species (an application of the “steady-state approximation” frequently used in chemical kinetics28). Another ramification of Eq. (8) is that one would expect the diffusive motions of the Al31 and Si41 species to be decoupled electrically, i.e., the rapid motions of the other ionic species would disallow the accumulation of an electrical potential. Nevertheless, the motions of Al31 and Si41 cations are coupled by a molar-flux constraint, which is the second continuity condi￾tion. This constraint means that there must be a one-to-one substitution of Al31 and Si41 cations between feldspar and mica; that is, maintenance of the mica and feldspar structures requires that the tetrahedral cation fluxes be coupled. Mathematically, this constraint is articulated as jAl31 5 2jSi41 (9) One can substitute the Fick–Einstein flux equations for the Al31 and Si41 species from Eqs. (6) into Eq. (9) and, realizing that the electrical potential is mitigated by the rapid motion of the alkali and alkaline-earth species, solve for the binary chemical (inter)dif￾fusion coefficient D˜ , which, because of the simple molar-flux constraint, results in a simple Nernst–Planck form, i.e., D˜ 5 DAl31DSi41 XAl31DAl31 1 XSi41DSi41 (10) where X is the mole fraction. The above-given argument, given the assumptions noted, is rigorous; thus, the interdiffusion problem simplifies to one that can be analyzed using the typically applied form of Fick’s first law; that is, for each phase, jSi41 5 2D˜ dXSi41 dj (11) with a similar expression for jAl31. Because of the differences in the structures of the two phases in the reaction couple, the intrinsic diffusion coefficients for the Al31 and Si41 cations will be different in each phase. Furthermore, as is readily apparent from the diffusion profiles presented in, e.g., Fig. 3(a), the concentrations of these two tetrahedral cations vary with the distance j away from the interface (which is j 5 0). Thus, one realizes that D˜ feld Þ D˜ mica (where the superscripts are associated with feldspar and mica phases, respectively). Furthermore, neither D˜ feld nor D˜ mica has a unique value; instead, each is a function of distance, time, and temperature. The diffusion profile, of Si41, for example, in each phase is characterized by the error-function form that is the solution to Fick’s second law. In this problem, however, the continuity condition (Eq. (9)) must be active everywhere, including at the interface. The significant consequence of this fact is that the specific two-phase (local) equilibrium established at the interface is a function of the initial compositions of the reactants and the relative values of D˜ feld and D˜ mica at j 5 0. Thus, writing Eq. (9) specifically for the Si41 flux at the interface (using the Eq. (11) form for flux), D˜ feld dXSi41 feld dj 5 D˜ mica dXSi41 mica dj (12) one can use the derivative of the error-function form of XSi41(j,t) to solve for the relative values of D˜ feld and D˜ mica. Such an approach has been fully articulated by Jost29 and Swenson et al.;30 for this mica–feldspar interdiffusion problem, the result is XSi41,int feld 2 XSi41,bulk feld XSi41,bulk mica 2 XSi41,int mica 5 S D˜ mica D˜ feld D 1/ 2 (13) where the subscript “int” denotes a value at the interface and the subscript “bulk” denotes a value associated with a reactant. In application to the diffusion data presented in Tables I and II, for the reaction of stabilized celsian with fluorokinoshitalite at 1300°C, XSi41,int feld 5 0.169, XSi41,bulk feld 5 0.185, XSi41,int mica 5 0.108, and XSi41,bulk mica 5 0.101; these values, when placed in Eq. (13), give D˜ mica ' 5D˜ feld. A simple comparison by inspection of the gradients of Si41 composition at j 5 0 in Fig. 3(a) (see Eq. (12)) supports a relative difference of this magnitude. Application of Eq. (13) to the data at 1200°C (Tables III and IV) gives D˜ mica ' 2D˜ feld. These differences in interdiffusion coefficients for the tetrahedral species are consistent with the limited database for similar inter￾diffusion reactions in metamorphic rock assemblages.31 V. Summary and Comment The results of this investigation illustrate two different aspects of the petromimetic approach to the successful engineering of functional fluoromica-interphase/silicate-matrix interfaces for ap￾plication in an alumina-fiber ceramic composite. The first aspect demonstrates the necessity of chemical buffering—i.e., the need for a polyphase matrix that includes both spinel and forsterite—to stabilize the fluoromica interphase structurally against degradation due to alumina- or silica-excess feldspar-matrix stoichiometries. The MgO additions decrease the activity of the excess species by com￾bining to form either spinel or forsterite. Thus, the thermodynamic Table III. Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite Reacted at 1200°C Ion species Composition (wt%) Stabilized celsian Fluorokinoshitalite Bulk Interface Interface Bulk Ba21 13.52 6 0.10 25.42 6 0.10 20.78 6 0.58 27.29 6 0.46 K1 5.13 6 0.10 1.31 6 0.10 1.59 6 0.16 0.05 6 0.05 Sr21 7.21 6 0.10 5.32 6 0.10 0.57 6 0.13 0.13 6 0.11 Mg21 0.00 0.06 6 0.10 14.42 6 0.18 13.45 6 0.15 Al31 13.34 6 0.10 14.23 6 0.10 9.90 6 0.17 10.91 6 0.38 Si41 21.45 6 0.10 17.64 6 0.10 13.11 6 0.13 11.02 6 0.20 O22 40.58 6 0.10 37.00 6 0.10 33.27 6 0.71 32.11 6 0.19 F2 0.00 0.00 5.63 6 0.12 5.25 6 0.08 Total 100.91 6 0.10 100.97 6 0.10 99.73 6 0.09 100.23 6 0.55 Table IV. Stoichiometry of Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite Reacted at 1200°C Composition Celsian, (BaaKbSrcMgd)(AleSif )O8 Mica, (BaaKbSrc)Mgd(AleSif )O10Fg Bulk Interface Interface Bulk a 0.31 0.64 0.73 0.99 b 0.41 0.12 0.19 0.00 c 0.26 0.21 0.04 0.00 d 0.00 0.01 2.85 2.75 e 1.55 1.83 1.77 2.01 f 2.41 2.17 2.25 1.95 g 1.42 1.38 2294 Journal of the American Ceramic Society—King et al. Vol. 83, No. 9