eptember 2000 ns and equilibria between Fl as and Silicate Matrices 2293 Table I. Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite reacted at 1300oc Stabilized celsian Fluorokinoshitalite lon species Bulk Interface Interface Bulk 13.04±0.80 22.86±3.41 19.95±1.06 27.22±0.4 5.07±0.56 2.07±0.4 8.06±0.75 5.94±0.12 0.71±0.1 15.00±0.44 13.50±0.2 13.57±008 17.88±1.33 61±0.50 10.90±0.29 962±0.22 59±1.14 31.94±1.4 22±0.32 Total 100.07±0.69 9964±0.15 9955±0.41 9961±0.14 Table l. Stoichiometry of Bulk and Interfacial allows the driving force for chemical diffusion to be reduced to the Compositions of K-Sr Stabilized Celsian and adients in concentration only Fluorokinoshitalite reacted at 1300oc One can describe the motion of an individual ionic species i using the Fick/Einstein relationship(Fick's first law). In this relationship, a Ba,K.Sr,Mg,XALSi)O,(Ba, K,Sr )Mg/AI si)o oF. flux is driven by the gradient in electrochemical potential Bulk do a 0.31 A=、SD9%D(+ZF 000 0.04 0.02 where j, is the flux of the ith species, c the concentration, D the 0 2.85 defg intrinsic(self-)diffusion coefficient, m the electrochemical poten- 1.91 tial(which consists of the chemical-potential (u)and electrical potential(c) components), Z the valence, s the distance, F the Faradays constant, R the universal gas constant, and T the temperature. Thus, for the diffusing species in the stabilized- elsian/fluorokinoshitalite reaction couple displayed in Fig. 3(a), the fluxes in both phases can be described as K-rich region indicates that Ba cations have not yet reached the center section of the grain in appreciable quantities. Not surprisingly, 2+DBa+ dnBi+ the more-spacious interlayer planes allow cationic interdiffusion to JBa2+ proceed with relative ease, compared with diffusion through the more densely packed and strongly bonded tetrahedral and octahedral sheets CK+DK+ dnk of the phyllosilicate; interdiffusing cations, particularly K+ and Ba2+ 丿B (6b) cross the stabilized-celsian/fluoromica interface will be slowed bstantially when encountering phyllosilicate grains oriented parallel Dot-d (or almost parallel)to the interface IV. Discussio CAl+ DAP+ dmap+ JAIS Characterization of the Multicomponent Interdiffusion The experimental results of the reaction olid-solution CS++DSH+ amsH K-Ba feldspar and solid-solution K-Ba tri Js clearly demonstrate coupled cationic interdi exchange of K+ and Si+ cations for Ba 1+cations. A flux equation for the 02- species is included because the limited Therefore, a diffusion model that addresses quaternary systems is database available for ionic diffusion in silicate necessary to describe the interdiffusive response at the interface that the intrinsic mobility of the o- igorously. Because of the complexities that are involved in at of the tetrahedral cation s anion may perhaps be faster describing the related motion of four cationic species, however continuity conditions should be considered for this anal some general assumptions can be made to develop a tractable first, which can be used to greatly simplify the problem, description of the phenomenon. The first assumption is that the is charge neutrality, that is reaction-couple substrates (i.e, the reactants)act as infinite sources of the diffusing species. This assumption is justified easily ∑:=002/m2+jk+-2ip-=-3Ap+-4/s(7) considering the minute diffusion distances relative to the overall One then can substitute Eqs. (6)into Eq.(7). Simplification depth( thickness)of the reactants. The second assumption is that cal equilibrium is maintained at all times, despite the significant becomes involved when one realizes that concentration gradients that evolve during the reaction. While a CBa2+DBa2+, CK+DK+>>co2-Do2->>CAJ+ DAF+, CsH+Ds:+(8) standard assumption for diffusion analyses, this assumption in- cludes the fact that, on initiation and continuation of the reaction That is, the products of concentration and mobility of the interlayer he new (reacted) interfacial com of both mica and cations and, perhaps, of oxygen, far outstrip those of the remain fixed. The third assumption is that tetrahedral cations Al+ and Si+. If such is the case, then or lution behavior adequately de the diffusion process, cannot, in this interdiffusion problem, sustain an electrochemicalK1-rich region indicates that Ba21 cations have not yet reached the center section of the grain in appreciable quantities. Not surprisingly, the more-spacious interlayer planes allow cationic interdiffusion to proceed with relative ease, compared with diffusion through the more densely packed and strongly bonded tetrahedral and octahedral sheets of the phyllosilicate; interdiffusing cations, particularly K1 and Ba21, across the stabilized-celsian/fluoromica interface will be slowed substantially when encountering phyllosilicate grains oriented parallel (or almost parallel) to the interface. IV. Discussion: Characterization of the Multicomponent Interdiffusion The experimental results of the reaction between solid-solution K-Ba feldspar and solid-solution K-Ba trioctahedral fluoromica clearly demonstrate coupled cationic interdiffusion involving the exchange of K1 and Si41 cations for Ba21 and Al31 cations. Therefore, a diffusion model that addresses quaternary systems is necessary to describe the interdiffusive response at the interface rigorously. Because of the complexities that are involved in describing the related motion of four cationic species, however, some general assumptions can be made to develop a tractable description of the phenomenon. The first assumption is that the reaction-couple substrates (i.e., the reactants) act as infinite sources of the diffusing species. This assumption is justified easily, considering the minute diffusion distances relative to the overall depth (thickness) of the reactants. The second assumption is that local equilibrium is maintained at all times, despite the significant concentration gradients that evolve during the reaction. While a standard assumption for diffusion analyses, this assumption in￾cludes the fact that, on initiation and continuation of the reaction, the new (reacted) interfacial compositions of both mica and feldspar remain fixed. The third general assumption is that ideal-solution behavior adequately describes the diffusion process, a point easily justified in that, given the lack of any transition￾metal cation species, the point-defect concentrations, by whose motion chemical diffusion occurs, are very small; this assumption allows the driving force for chemical diffusion to be reduced to the gradients in concentration only. One can describe the motion of an individual ionic species i using the Fick/Einstein relationship (Fick’s first law). In this relationship, a flux is driven by the gradient in electrochemical potential: ji 5 2 ciDi RT dhi dj 5 2 ciDi RT S dmi dj 1 ZiF df dj D (5) where ji is the flux of the ith species, c the concentration, D the intrinsic (self-)diffusion coefficient, h the electrochemical poten￾tial (which consists of the chemical-potential (m) and electrical￾potential (f) components), Z the valence, j the distance, F the Faraday’s constant, R the universal gas constant, and T the temperature. Thus, for the diffusing species in the stabilized￾celsian/fluorokinoshitalite reaction couple displayed in Fig. 3(a), the fluxes in both phases can be described as jBa21 5 2 cBa21DBa21 RT dhBa21 dj (6a) jK1 5 2 cK1DK1 RT dhK1 dj (6b) jO22 5 2 cO22DO22 RT dhO22 dj (6c) jAl31 5 2 cAl31DAl31 RT dhAl31 dj (6d) jSi41 5 2 cSi41DSi41 RT dhSi41 dj (6e) A flux equation for the O22 species is included because the limited database available for ionic diffusion in silicate minerals suggests that the intrinsic mobility of the O22 anion may perhaps be faster than that of the tetrahedral cations.26 Two continuity conditions should be considered for this analy￾sis. The first, which can be used to greatly simplify the problem, is charge neutrality; that is, O zi ji 5 0 or 2jBa21 1 jK1 2 2jO22 5 23jAl31 2 4jSi41 (7) One then can substitute Eqs. (6) into Eq. (7). Simplification becomes involved when one realizes that cBa21DBa21 , cK1DK1..cO22DO22..cAl31DAl31 , cSi41DSi41 (8) That is, the products of concentration and mobility of the interlayer cations and, perhaps, of oxygen,26 far outstrip those of the tetrahedral cations Al31 and Si41. If such is the case, then one cannot, in this interdiffusion problem, sustain an electrochemical￾potential gradient of the Ba21, K1, or O22 species. Therefore, the Gibbs energy of the interdiffusion reaction will be dissipated by the diffusion of the tetrahedral cations (see Schmalzried27); i.e., no Table I. Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite Reacted at 1300°C Ion species Composition (wt%) Stabilized celsian Fluorokinoshitalite Bulk Interface Interface Bulk Ba21 13.04 6 0.80 22.86 6 3.41 19.95 6 1.06 27.22 6 0.49 K1 5.07 6 0.56 2.22 6 0.75 2.07 6 0.49 0.08 6 0.08 Sr21 8.06 6 0.75 5.94 6 0.12 0.71 6 0.15 0.26 6 0.09 Mg21 0.19 6 0.02 0.36 6 0.24 15.00 6 0.44 13.50 6 0.21 Al31 13.25 6 0.06 13.57 6 0.08 9.48 6 0.43 10.29 6 0.13 Si41 20.95 6 0.22 17.88 6 1.33 12.61 6 0.50 10.90 6 0.29 O22 39.62 6 0.22 36.98 6 1.29 34.59 6 1.14 31.94 6 1.48 F2 0.00 0.00 7.22 6 0.32 6.36 6 0.25 Total 100.07 6 0.69 99.64 6 0.15 99.55 6 0.41 99.61 6 0.14 Table II. Stoichiometry of Bulk and Interfacial Compositions of K-Sr Stabilized Celsian and Fluorokinoshitalite Reacted at 1300°C Composition Celsian, (BaaKbSrcMgd)(AleSif )O8 Mica, (BaaKbSrc)Mgd(AleSif )O10Fg Bulk Interface Interface Bulk a 0.31 0.57 0.67 0.99 b 0.42 0.20 0.25 0.02 c 0.30 0.23 0.04 0.02 d 0.03 0.05 2.85 2.21 e 1.59 1.74 1.62 1.91 f 2.41 2.20 2.08 1.95 g 1.75 1.68 September 2000 Thermochemical Reactions and Equilibria between Fluoromicas and Silicate Matrices 2293