------------------------------------------------------------------------- ! this file is an annotated print file generated in sample.3. ! Comment lines begin with an exclamation point. ! The calculation is of a Schreinemakers P-T diagram ! for the water-saturated system MGO-FEO-AL2O3-KALO2-SIO2, with the additional ! constraints that: ! 1) a pure SIO2 phase (Q,bQ) is stable with all assemblages. ! 2) the phase that coexists with this SIO2 phase on the SIO2-AL2O3 join ! (Ky,Sil,And,Phyl,Dia,Co,Kao, etc) is stable with all assemblages. ! 3) the phase that coexists with the above two phases on the KAlO2-AL2O3-SIO2 ! join (Kspar,Mu, etc) is stable with all assemblages. ! This implies the component saturation heirarchy SIO2-AL2O3-KALO2, with two ! thermodynamic components FeO and MgO. In other words, the calculation is of ! the P-T phase relations of the phases which would coexist with the phase on the ! Al2O3 apex of the phase diagrams calculated in sample.session2 if the ! roles of Al2O3 and KAlO3 were interchanged in in2.dat. This has been ! done in the file in4.dat, which you can try out if you like. ! Note that in changing the component saturation heirarchy has profound ! effects on the calculated phase relations for the system. ! (Try it as an aid to learning how to run Vertex). ! You can do the same kind of calculation for the J B. Thompson AFM ! projection done in sample.5 ! The first portion of the output is basically an echo of the users ! input, and is essentially identical to that in print2.ou2. For ! additional clarification see print2.out and documentation chapter 5. ! The same warning message as for sample.2 ** warning ver111 ** the following endmembers are missing for solution GrPyAl(B) gr it will be treated as a simpler solution between endmembers: py alm ----------------------------------------------------------------- summary for the 1st calculation follows: ----------------------------------------------------------------- problem title: test 3 thermodynamic data base from: HOLLAND AND POWELL 1989 fluid equation of state from: holland and powell, 1990 independently constrained potentials: T(K) P(bars) X(CO2) saturated phase components: H2O saturated or buffered components: ! with the above restrictions the system has only two thermodynamic ! components, consequently compositional variations can be shown ! along the FeO-MgO binary. invariant points will involve 4 phases (in ! addition to the four phases consistent with the saturation constraints), ! likewise nondegenerate univariant reactions will involve three ! phases. SIO2 AL2O3 KALO2 components with unconstrained potentials: FEO MGO phases and (projected) mol fraction MGO : feo 0.000 phl 1.000 ann 0.000 clin 1.000 daph 0.000 en 1.000 fs 0.000 py 1.000 alm 0.000 ap 1.000 fap 0.000 cumm 1.000 grun 0.000 crd 1.000 fcrd 0.000 mctd 1.000 fctd 0.000 mst 1.000 fst 0.000 ta 1.000 fta 0.000 br 1.000 sp 1.000 herc 0.000 mcar 1.000 fcar 0.000 per 1.000 da93 0.062 da87 0.125 da81 0.187 da75 0.250 da68 0.312 da62 0.375 da56 0.437 da50 0.500 da43 0.563 da37 0.625 da31 0.688 da24 0.750 da18 0.813 da12 0.875 da 6 0.938 ph93 0.938 ph87 0.875 ph81 0.813 ph75 0.750 ph68 0.688 ph62 0.625 ph56 0.563 ph50 0.500 ph43 0.437 ph37 0.375 ph31 0.312 ph24 0.250 ph18 0.187 ph12 0.125 ph 6 0.062 fs91 0.083 fs83 0.166 fs75 0.250 fs66 0.333 fs58 0.417 fs50 0.500 fs41 0.583 fs33 0.667 fs24 0.750 fs16 0.834 fs 8 0.917 fc91 0.083 fc83 0.167 fc75 0.250 fc66 0.333 fc58 0.417 fc50 0.500 fc41 0.583 fc33 0.667 fc24 0.750 fc16 0.833 fc 8 0.917 fc93 0.062 fc87 0.125 fc81 0.187 fc75 0.250 fc68 0.312 fc62 0.375 fc56 0.437 fc50 0.500 fc43 0.563 fc37 0.625 fc31 0.688 fc24 0.750 fc18 0.813 fc12 0.875 fc 6 0.938 cu93 0.938 cu87 0.875 cu81 0.813 cu75 0.750 cu68 0.688 cu62 0.625 cu56 0.563 cu50 0.500 cu43 0.437 cu37 0.375 cu31 0.312 cu24 0.250 cu18 0.187 cu12 0.125 cu 6 0.062 ap91 0.917 ap83 0.834 ap75 0.750 ap66 0.667 ap58 0.583 ap50 0.500 ap41 0.417 ap33 0.333 ap24 0.250 ap16 0.166 ap 8 0.083 en90 0.900 en80 0.800 en70 0.700 en60 0.600 en50 0.500 en39 0.400 en29 0.300 en19 0.200 en 9 0.100 ft91 0.083 ft83 0.167 ft75 0.250 ft66 0.333 ft58 0.417 ft50 0.500 ft41 0.583 ft33 0.667 ft24 0.750 ft16 0.833 ft 8 0.917 sp91 0.917 sp83 0.834 sp75 0.751 sp66 0.667 sp58 0.584 sp50 0.500 sp41 0.416 sp33 0.333 sp24 0.249 sp16 0.166 sp 8 0.083 fc91 0.083 fc83 0.167 fc75 0.250 fc66 0.333 fc58 0.417 fc50 0.500 fc41 0.583 fc33 0.667 fc24 0.750 fc16 0.833 fc 8 0.917 al93 0.062 al87 0.124 al81 0.187 al75 0.249 al68 0.312 al62 0.375 al56 0.437 al50 0.500 al43 0.563 al37 0.625 al31 0.688 al24 0.751 al18 0.813 al12 0.876 al 6 0.938 phases on saturation and buffering surfaces: ! note that the choice of saturated phases has become more complex. q bq coe pyhl and ky sill cor mu kf san excluded phases: sio2 al2o3 mgo k2o cel fcel sdph east ames fame kals lc mgts c-en fo fa tats ftat chr dia k2o ----------------------------------------------------------------- ! This is the beginning of calculated results, the structure ! of the output is as described for print.out1 ---------------------------------------------------------------- ! First the stable chemographic phase relations at the minimum P and T. the stable assemblages at: T(K) = 773.000 P(bars) = 2000.00 X(CO2) = 0. are: ! No variance flags are output for binary chemographies and ! the phases are written in the order that they occur along ! the binary. ! All phases coexist with q, and, and mu. The ! pseudocompoundd chemography indicates that Chloritoid with ! a composition of X(Fe)= 100% to 91% is stable, the Mg-rich ! chloritoid may coexist with a chlorite with X(Fe)=75%, and that ! chlorite is stable with X(Fe)=75% to 0%. Note that because the ! pseudocompounds discretize continuous variations, the resolution ! on the continuous variation is determined by how the compounds ! are defined. Here the compounds are spaced at about 10 mole % ! intervals, thus stability of fc91 does not indicate that this ! is the true limiting composition, but rather that fc81 is ! unstable, the true limiting composition is most probably between ! fc91 and fc81 at about 86% Fe-component. fctd fc91 da75 da68 da62 da56 da50 da43 da37 da31 da24 da18 da12 da 6 clin these assemblages are compatible with the following phases or species determined by component saturation or buffering constraints: q and mu ** immiscibility occurs in one or more of the stable solution phases ** ---------------------------------------------------------------------- The T(K) -P(bars) loci of (pseudo-) univariant fields follow: the fields are subject to the constraint(s): X(CO2) = 0. These fields are consistent with saturation or buffering constraints on the component(s): SIO2 AL2O3 KALO2 NOTE: For each field the values of the dependent extensities are output for the first equilibrium condition, in general these properties vary with the independent potentials. Reaction equations are written such that the high T(K) assemblage is on the right of the = sign ---------------------------------------------------------------------- ! the first reaction found is a degenerate singular reaction which ! limits the stability ferro-chloritoid in the FeO subsystem. ! each univariant curve is given a numeric label with two integers, ! the first is an equilibrium identifier, and the second is a ! variance indicator. The variance indicator is one if every ! compound in the equilibrium represents a unique phase, i.e., ! the equilibrium is a true univariant equilibrium. The variance ! indicator is two if more than one compounds represent the ! same phase, as in equilibrium 7 below. In such cases the ! equilibrium curve is, usually, a contour of divariant or higher ! variance phase field. ( 1-1) Ctd(i)(fctd) = GrPyAl(B)(alm) Alpha(-3.00, 1.00) Delta( SIO2 ) = 2.00 (saturated composant=q ) Delta( AL2O3) =-2.00 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-3.00 (saturated phase component) Delta(-V(j/b)) = 4.87 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-227. (dependent conjugate of T(K) ) 791.535 2000.00 795.719 2200.00 799.709 2400.00 801.640 2500.00 802.590 2550.00 802.597 2550.39 802.598 2550.44 802.599 2550.46 the equilibrium extends to invariant point ( 1) ! the equilibrium is traced to the FeO Garnet+Staurolite+Chloritoid ! invariant point, you can tell that this is a degenerate invariant ! point because the compound assemblage represents only three true ! phases, i.e., fctd and fc91 both represent chloritoid. ------ equilibria about invariant point ( 1): Ctd(i)(fctd) Ctd(i)(fc91) GrPyAl(B)(alm) St(i)(fst) are listed below: ! note that this reaction only limits the Fe-chloritoid endmember, but ! more magnesian ctd (fc91) is still stable. ( 2-1) Ctd(i)(fctd) = St(i)(fst) ! this equilibrium initially has a negative Clapeyron slope, the ! slope changes to positive when the And=Ky transition occurs, note ! that although vertex recognizes this, it doesn't tell you (see ! plot (a)). Alpha(-4.00, 1.00) Delta( SIO2 ) =-1.50 (saturated composant=q ) Delta( AL2O3) = 5.00 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-2.00 (saturated phase component) Delta(-V(j/b)) =-.718 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-160. (dependent conjugate of T(K) ) 802.599 2550.46 801.594 2750.46 800.396 2950.46 799.026 3150.46 797.500 3350.46 795.834 3550.46 794.040 3750.46 792.132 3950.46 790.118 4150.46 791.655 4350.46 793.738 4550.46 795.772 4750.46 797.762 4950.46 799.711 5150.46 801.620 5350.46 803.491 5550.46 805.328 5750.46 807.131 5950.46 808.902 6150.46 810.643 6350.46 812.355 6550.46 814.039 6750.46 815.697 6950.46 817.330 7150.46 818.938 7350.46 820.523 7550.46 822.084 7750.46 823.624 7950.46 825.143 8150.46 826.641 8350.46 828.119 8550.46 829.578 8750.46 831.018 8950.46 832.439 9150.46 833.843 9350.46 835.230 9550.46 836.599 9750.46 837.952 9950.46 838.285 10000.0 ( 3-1) St(i)(fst) = GrPyAl(B)(alm) ! the p-T coordinates of this equilibrium pass through three saturated ! composant transitions, And=Sil, Kf=Sa, and Sa=Kf, all ! at about 7 to 8 kbar. Alpha(-1.00, 1.33) Delta( SIO2 ) = 4.17 (saturated composant=q ) Delta( AL2O3) =-7.67 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-2.00 (saturated phase component) Delta(-V(j/b)) =-6.30 (dependent conjugate of P(bars) ) Delta(S(j/k) ) = 136. (dependent conjugate of T(K) ) 802.599 2550.46 811.858 2750.46 811.930 2752.03 811.966 2752.81 811.984 2753.20 811.986 2753.25 811.987 2753.27 811.988 2753.28 ! although the reaction for this equilibrium does not involve ! chloritoid (ctd), the equilibrium occurs with an Fe-rich ctd compound ! (fc91). Vertex actually traces the conditions for this equilibrium, and ! not simply the reaction; thus, when vertex finds that fc91 is no longer ! stable it reports an invariant point. the alm=fst reaction can be traced ! stably through the invariant point, but beyond the invariant point the ! equilibrium no longer occurs with ctd, and is, in fact, a different ! equilibrium. the equilibrium extends to invariant point ( 2) ! this point is also degenerate, as can be recognized ! by the number of true phases represented (i.e., 3, ctd, gt, st), ! but in this case the point actually represents a singular point. ------ ------ equilibria about invariant point ( 2): Ctd(i)(fc91) GrPyAl(B)(alm) St(i)(fst) Chl(i)(da81) are listed below: ! this is the first nondegenerate univariant reaction and defines ! the thermal limit of ctd (i.e., ctd=st+gt). the composition of ! the ctd at this limit is around 91% Fe (+/-5%) for the P-T conditions ! listed. ( 4-1) Ctd(i)(fc91) = GrPyAl(B)(alm) Chl(i)(da81) Alpha(-11.2, 2.08, 1.00) Delta( SIO2 ) = 6.16 (saturated composant=q ) Delta( AL2O3) =-8.16 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-7.25 (saturated phase component) Delta(-V(j/b)) = 13.5 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-562. (dependent conjugate of T(K) ) 811.988 2753.28 807.112 2553.28 802.104 2353.28 799.545 2253.28 798.900 2228.28 798.576 2215.78 798.414 2209.53 798.332 2206.41 798.330 2206.31 the equilibrium extends to invariant point ( 3) ( 5-1) Ctd(i)(fc91) = St(i)(fst) Chl(i)(da81) Alpha(-11.2, 1.56, 1.00) Delta( SIO2 ) =-.342 (saturated composant=q ) Delta( AL2O3) = 3.81 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-4.12 (saturated phase component) Delta(-V(j/b)) = 3.84 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-352. (dependent conjugate of T(K) ) 811.988 2753.28 812.005 2754.88 812.023 2756.48 812.040 2758.08 812.057 2759.68 812.075 2761.28 812.092 2762.88 812.110 2764.48 812.127 2766.08 812.144 2767.68 812.162 2769.28 812.179 2770.88 812.196 2772.48 812.214 2774.08 812.231 2775.68 812.248 2777.28 812.265 2778.88 812.283 2780.48 812.300 2782.08 812.317 2783.68 812.334 2785.28 812.352 2786.88 812.369 2788.48 812.386 2790.08 812.403 2791.68 812.404 2791.78 812.405 2791.83 the equilibrium extends to invariant point ( 4) ( 3-1) St(i)(fst) = GrPyAl(B)(alm) Alpha(-1.00, 1.33) Delta( SIO2 ) = 4.17 (saturated composant=q ) Delta( AL2O3) =-7.67 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-2.00 (saturated phase component) Delta(-V(j/b)) =-6.22 (dependent conjugate of P(bars) ) Delta(S(j/k) ) = 135. (dependent conjugate of T(K) ) 811.988 2753.28 812.062 2754.88 812.136 2756.48 812.209 2758.08 812.283 2759.68 812.357 2761.28 812.431 2762.88 812.505 2764.48 812.579 2766.08 812.653 2767.68 812.727 2769.28 812.800 2770.88 812.874 2772.48 812.948 2774.08 813.022 2775.68 813.096 2777.28 813.170 2778.88 813.244 2780.48 813.253 2780.68 813.257 2780.78 813.260 2780.83 the equilibrium extends to invariant point ( 5) ------ ------ equilibria about invariant point ( 3): Ctd(i)(fc91) GrPyAl(B)(alm) Chl(i)(da81) Chl(i)(da87) are listed below: . . abridged output . . ( 6-1) Ctd(i)(fc91) = GrPyAl(B)(alm) Chl(i)(da87) Alpha(-7.50, 0.832, 1.00) Delta( SIO2 ) = 3.66 (saturated composant=q ) Delta( AL2O3) =-5.66 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-3.50 (saturated phase component) Delta(-V(j/b)) = 9.15 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-297. (dependent conjugate of T(K) ) 798.330 2206.31 792.105 2006.31 791.907 2000.00 ( 7-2) Ctd(i)(fc91) Chl(i)(da81) = Chl(i)(da87) Alpha(-3.00, -.400, 1.00) Delta( SIO2 ) = 1.20 (saturated composant=q ) Delta( AL2O3) =-2.40 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-.600 (saturated phase component) Delta(-V(j/b)) = 3.18 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-67.7 (dependent conjugate of T(K) ) 798.330 2206.31 788.892 2006.31 788.593 2000.00 ! this next reaction illustrates a common problem with pseudocompounds, ! namely that two compounds of different phases have nearly identical ! compositions. This can sometimes result in misleading in that ! the stoichimetric coefficient of one compound may not differ ! significantly from zero, this in turn can sometimes cause numeric ! instabilities. The best solution to this problem is to make ! subdivision schemes which do not generate pseudocompounds for ! different solutions with the same Mg/Fe ratio (the easiest way ! to do this is with cartesian subdivision, see documentation chapter ! 4). ( 14-1) Ctd(i)(fc91) = Chl(i)(da75) St(i)(fs91) Alpha(-4.00, 0.649E-03, 1.00) Delta( SIO2 ) =-1.50 (saturated composant=q ) Delta( AL2O3) = 5.00 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-2.00 (saturated phase component) Delta(-V(j/b)) =-1.08 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-155. (dependent conjugate of T(K) ) 814.183 3119.52 813.903 3159.52 813.760 3179.52 813.688 3189.52 813.652 3194.52 813.643 3195.77 813.641 3196.08 813.640 3196.24 the equilibrium extends to invariant point ( 8) ( 37-2) Chl(i)(da62) = GrPyAl(B)(al93) Chl(i)(da56) Alpha(-1.20, 0.333, 1.00) Delta( SIO2 ) =0.267 (saturated composant=q ) Delta( AL2O3) =0.133 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-.800 (saturated phase component) Delta(-V(j/b)) =0.214 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-47.6 (dependent conjugate of T(K) ) 848.628 3561.24 847.652 3361.24 846.507 3161.24 846.351 3136.24 846.341 3134.68 846.336 3133.90 846.336 3133.80 846.335 3133.77 the equilibrium extends to invariant point ( 19) . . output abridged . . ! this is the first nondegenerate (i.e.,nondegenerate (i.e., four-phase) ! invariant point. Each univariant curve defines the limits of stability for an ! assemblage inside the FeO-MgO binary. equilibria about invariant point ( 18): St(i)(fs91) GrPyAl(B)(al93) Chl(i)(da56) Bio(i)(ph43) are listed below: ( 44-1) St(i)(fs91) = GrPyAl(B)(al93) Bio(i)(ph43) Alpha(-13.4, 16.8, 1.00) Delta( SIO2 ) = 53.8 (saturated composant=q ) Delta( AL2O3) =-105. (saturated composant=and ) Delta( KALO2) = 1.00 (saturated composant=mu ) Delta( H2O ) =-26.8 (saturated phase component) Delta(-V(j/b)) = 82.0 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-.176E+04 (dependent conjugate of T(K) ) 862.551 3844.86 871.881 4044.86 872.464 4057.36 872.756 4063.61 872.902 4066.73 872.920 4067.12 the equilibrium extends to invariant point ( 25) ( 45-1) St(i)(fs91) Chl(i)(da56) = Bio(i)(ph43) Alpha(-.203E-04, -.600, 1.00) Delta( SIO2 ) =-1.20 (saturated composant=q ) Delta( AL2O3) =-1.60 (saturated composant=and ) Delta( KALO2) = 1.00 (saturated composant=mu ) Delta( H2O ) =-2.40 (saturated phase component) Delta(-V(j/b)) = 2.83 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-146. (dependent conjugate of T(K) ) 862.551 3844.86 863.324 3884.86 863.421 3889.86 863.469 3892.36 863.493 3893.61 863.499 3893.92 863.501 3894.00 ( 46-1) GrPyAl(B)(al93) Chl(i)(da56) = Bio(i)(ph43) Alpha(-.255E-04, -.600, 1.00) Delta( SIO2 ) =-1.20 (saturated composant=q ) Delta( AL2O3) =-1.60 (saturated composant=and ) Delta( KALO2) = 1.00 (saturated composant=mu ) Delta( H2O ) =-2.40 (saturated phase component) Delta(-V(j/b)) = 2.83 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-146. (dependent conjugate of T(K) ) 862.551 3844.86 861.774 3804.86 860.993 3764.86 860.207 3724.86 860.109 3719.86 860.060 3717.36 860.035 3716.11 860.029 3715.80 the equilibrium extends to invariant point ( 26) ------ ( 18-2) Chl(i)(da68) Ctd(i)(fc91) = Chl(i)(da75) Alpha(-.727, -1.36, 1.00) Delta( SIO2 ) =0.546 (saturated composant=q ) Delta( AL2O3) =-1.09 (saturated composant=and ) Delta( KALO2) = 0. (saturated composant=mu ) Delta( H2O ) =-.273 (saturated phase component) Delta(-V(j/b)) = 1.41 (dependent conjugate of P(bars) ) Delta(S(j/k) ) =-31.8 (dependent conjugate of T(K) ) 773.000 2272.15 780.500 2441.27 788.000 2611.10 795.500 2781.59 803.000 2952.65 810.500 3124.25 812.375 3167.23 813.312 3188.73 813.547 3194.11 813.605 3195.45 813.635 3196.12 813.638 3196.21 813.639 3196.23 813.640 3196.24 Network traced, resuming boundary search. ----------------------------------------------------------------------- (pseudo-) invariant points are summarized below: ( 1-1) Ctd(i)(fctd) Ctd(i)(fc91) GrPyAl(B)(alm) St(i)(fst) occurs at: T(K) = 802.599 P(bars) = 2550.46 X(CO2) = 0. ( 2-1) Ctd(i)(fc91) GrPyAl(B)(alm) St(i)(fst) Chl(i)(da81) occurs at: T(K) = 811.988 P(bars) = 2753.28 X(CO2) = 0. ( 3-2) Ctd(i)(fc91) GrPyAl(B)(alm) Chl(i)(da81) Chl(i)(da87) occurs at: T(K) = 798.330 P(bars) = 2206.31 X(CO2) = 0. ( 4-2) Ctd(i)(fc91) St(i)(fst) Chl(i)(da81) Chl(i)(da75) occurs at: T(K) = 812.405 P(bars) = 2791.83 X(CO2) = 0. ( 5-2) GrPyAl(B)(alm) Chl(i)(da81) St(i)(fst) Chl(i)(da75) occurs at: T(K) = 813.260 P(bars) = 2780.83 X(CO2) = 0. . . output abridged . . (135-1) Cumm(i)(cu93) Crd(i)(crd) Bio(i)(phl) Cumm(i)(cumm) occurs at: T(K) = 1066.14 P(bars) = 6213.81 X(CO2) = 0. ---------------------------------------------------------------- (pseudo-) invariant points are summarized below: ( 1-1) fctd fc91 alm fst ( 2-1) fc91 alm fst da81 ( 3-2) fc91 alm da81 da87 ( 4-2) fc91 fst da81 da75 ( 5-2) alm da81 fst da75 ( 6-2) fc91 fst da75 fs91 ( 7-2) alm da75 fst al93 ( 8-2) fc91 da75 fs91 da68 ( 9-2) fst da75 fs91 al93 ( 10-2) fc91 fs91 da68 da62 ( 11-2) da75 fs91 da68 al93 ( 12-2) fc91 fs91 da62 fc83 ( 13-2) fs91 da68 da62 al93 ( 14-2) fs91 da62 fc83 da56 ( 15-2) fs91 da62 al93 da56 ( 16-2) da68 da62 al93 ph31 ( 17-2) fs91 fc83 da56 da50 ( 18-1) fs91 al93 da56 ph43 ( 19-2) da62 al93 da56 ph37 ( 20-2) da68 da62 ph31 fc62 ( 21-2) da68 al93 ph31 ph24 ( 22-2) da62 al93 ph31 ph37 ( 23-2) fs91 fc83 da50 fc75 ( 24-2) fs91 da56 da50 ph43 ( 25-2) fs91 al93 ph43 al87 ( 26-2) al93 da56 ph43 ph37 ( 27-2) da62 da56 ph37 fc56 ( 28-2) da68 ph31 fc62 ph24 ( 29-2) da62 ph31 fc62 fc56 ( 30-1) da68 al93 ph24 fc68 ( 31-2) al93 ph31 ph24 fc62 ( 32-2) da62 ph31 ph37 fc56 ( 33-2) al93 ph31 ph37 fc56 ( 34-2) fs91 da50 fc75 da43 ( 35-2) fs91 da50 ph43 ph50 ( 36-1) da56 da50 ph43 fc50 ( 37-2) fs91 ph43 al87 ph50 ( 38-2) al93 ph43 al87 ph37 ( 39-2) da56 ph43 ph37 fc50 ( 40-2) da56 ph37 fc56 fc50 ( 41-2) da68 fc62 ph24 fc68 ( 42-2) ph31 fc62 fc56 al93 ( 43-2) al93 ph24 fc68 fc62 ( 44-2) al93 ph37 fc56 fc50 ( 45-1) fs91 da50 da43 ph50 ( 46-2) da50 ph43 ph50 fc43 ( 47-2) da50 ph43 fc50 fc43 ( 48-2) fs91 al87 ph50 fs83 ( 49-2) ph43 al87 ph50 fc43 ( 50-2) al93 al87 ph37 fc50 ( 51-2) ph43 ph37 fc50 al87 ( 52-2) fc62 fc56 al93 sp16 ( 53-2) al93 fc68 fc62 sp 8 ( 54-2) al93 fc56 fc50 al87 ( 55-2) fs91 da43 ph50 ph56 ( 56-2) da50 da43 ph50 fc43 ( 57-2) ph43 fc50 fc43 al87 ( 58-2) fs91 ph50 fs83 ph56 ( 59-2) al87 ph50 fs83 al81 ( 60-2) al87 ph50 fc43 al81 ( 61-2) fc62 al93 sp16 sp 8 ( 62-2) fc56 al93 sp16 al87 ( 63-2) al93 fc68 sp 8 fc75 ( 64-2) fs91 da43 ph56 fs83 ( 65-2) da43 ph50 ph56 fc37 ( 66-2) da43 ph50 fc43 fc37 ( 67-2) ph50 fs83 ph56 al81 ( 68-2) ph50 fc43 al81 fc37 ( 69-2) al93 sp 8 fc75 fc81 ( 70-2) da43 ph56 fs83 da37 ( 71-2) da43 ph56 fc37 da37 ( 72-2) ph50 ph56 fc37 al81 ( 73-2) fs83 ph56 al81 al75 ( 74-2) al93 sp 8 fc81 alm ( 75-2) al93 fc75 fc81 alm ( 76-2) ph56 fs83 da37 ph62 ( 77-2) ph56 fc37 da37 fc31 ( 78-2) ph56 fc37 al81 al75 ( 79-2) fs83 ph56 al75 ph62 ( 80-2) sp 8 fc81 alm fc87 ( 81-2) ph56 da37 ph62 fc31 ( 82-2) fs83 da37 ph62 da31 ( 83-2) ph56 fc37 fc31 al75 ( 84-2) ph56 al75 ph62 fc31 ( 85-2) sp 8 alm fc87 herc ( 86-2) da37 ph62 fc31 da31 ( 87-1) fs83 ph62 da31 cu62 ( 88-2) al75 ph62 fc31 al68 ( 89-2) alm fc87 herc fc93 ( 90-2) ph62 fc31 da31 fc24 ( 91-2) ph62 da31 cu62 ph68 ( 92-2) al75 ph62 al68 ph68 ( 93-1) ph62 fc31 al68 cu62 ( 94-1) alm fc93 herc fcrd ( 95-2) ph62 fc31 fc24 cu62 ( 96-2) ph62 da31 fc24 ph68 ( 97-2) da31 cu62 ph68 cu68 ( 98-2) ph62 al68 ph68 al62 ( 99-2) ph62 al68 cu62 al62 (100-2) ph62 fc24 cu62 ph68 (101-2) da31 fc24 ph68 da24 (102-2) da31 ph68 cu68 da24 (103-2) ph62 ph68 al62 cu62 (104-2) fc24 cu62 ph68 cu68 (105-2) fc24 ph68 da24 fc18 (106-2) ph68 cu68 da24 ph75 (107-2) fc24 ph68 cu68 fc18 (108-2) ph68 da24 fc18 ph75 (109-2) cu68 da24 ph75 cu75 (110-2) ph68 cu68 fc18 ph75 (111-2) da24 fc18 ph75 da18 (112-2) da24 ph75 cu75 da18 (113-2) cu68 fc18 ph75 cu75 (114-2) fc18 ph75 da18 ph81 (115-2) ph75 cu75 da18 ph81 (116-2) fc18 ph75 cu75 ph81 (117-2) fc18 da18 ph81 fc12 (118-2) fc18 cu75 ph81 cu81 (119-2) fc18 ph81 fc12 cu81 (120-2) da18 ph81 fc12 da12 (121-2) ph81 fc12 cu81 ph87 (122-2) ph81 fc12 da12 ph87 (123-2) fc12 cu81 ph87 cu87 (124-2) fc12 da12 ph87 fc 6 (125-2) fc12 ph87 cu87 fc 6 (126-2) da12 ph87 fc 6 da 6 (127-2) ph87 cu87 fc 6 ph93 (128-2) ph87 fc 6 da 6 ph93 (129-2) cu87 fc 6 ph93 cu93 (130-2) fc 6 da 6 ph93 crd (131-2) fc 6 ph93 cu93 crd (132-2) da 6 ph93 crd clin (133-2) ph93 cu93 crd phl (134-1) ph93 crd clin phl (135-1) cu93 crd phl cumm ---------------------------------------------------------------- (pseudo-) univariant equilibria are summarized below: ( 1-1) Ctd(i)(fctd) = GrPyAl(B)(alm) ( 2-1) Ctd(i)(fctd) = St(i)(fst) ( 3-1) St(i)(fst) = GrPyAl(B)(alm) ( 4-1) Ctd(i)(fc91) = GrPyAl(B)(alm) Chl(i)(da81) ( 5-1) Ctd(i)(fc91) = St(i)(fst) Chl(i)(da81) ( 6-1) Ctd(i)(fc91) = GrPyAl(B)(alm) Chl(i)(da87) ( 7-2) Ctd(i)(fc91) Chl(i)(da81) = Chl(i)(da87) ( 8-2) Chl(i)(da87) = GrPyAl(B)(alm) Chl(i)(da81) ( 9-1) Ctd(i)(fc91) = St(i)(fst) Chl(i)(da75) ( 10-2) Ctd(i)(fc91) Chl(i)(da75) = Chl(i)(da81) ( 11-2) Chl(i)(da81) = St(i)(fst) Chl(i)(da75) ( 12-2) Chl(i)(da81) = GrPyAl(B)(alm) Chl(i)(da75) ( 13-2) Ctd(i)(fc91) St(i)(fst) = St(i)(fs91) . . output abridged . . (310-2) Bio(i)(ph93) Bio(i)(phl) = Cumm(i)(cu93) (311-1) Bio(i)(phl) = Crd(i)(crd) (312-1) Chl(i)(clin) = Bio(i)(phl) (313-1) Cumm(i)(cumm) = Crd(i)(crd) (314-1) Bio(i)(phl) = Cumm(i)(cumm) (315-2) Ctd(i)(fc75) Chl(i)(da37) = Chl(i)(da43) (316-2) Ctd(i)(fc66) = Ctd(i)(fc75) Chl(i)(da37) (317-2) Chl(i)(da31) Ctd(i)(fc66) = Chl(i)(da37) (318-2) Ctd(i)(fc58) = Chl(i)(da31) Ctd(i)(fc66) ----------------------------------------------------------------