Large negative values of Cpx end members propotions

[Anna Sapegina]

Greetings colleagues!

I know it's a lot massages from me on the forum last weeks.
I've read the topic about nagative poroptions of end memebers in spinel that is published here a time ago, but I observe the large values of negative propotions and it's confusing.
What is the right way to interpretate this data?

Title: osyb9

T = 1205,00 (C)  P = 9,000 (kbars)  log(10) f O2 = -7,58  delta HM = -4,92  NNO = -0,07  QFM = 0,00  COH = 1,83  IW = 4,11

Constraint Flags: fO2 path = QFM 

Liquid           mass = 27,95 (gm)  density = 3,09 (gm/cc)  viscosity = 1,49 (log 10 poise)     (analysis in wt %)
      G = -388332,13 (J)  H = -280978,92 (J)  S = 72,63 (J/K)  V = 9,05 (cc)  Cp = 38,42 (J/K) 
        SiO2   TiO2  Al2O3  Fe2O3  Cr2O3    FeO    MnO    MgO    NiO    CoO    CaO   Na2O    K2O   P2O5    H2O    CO2    SO3 Cl2O-1  F2O-1
       41,29   5,16  13,04   2,97   0,00  23,16   1,04   3,10   0,00   0,00   7,64   2,61   0,00   0,00   0,00   0,00   0,00   0,00   0,00

clinopyroxene    mass = 30,84 (gm)  density = 3,39 (gm/cc)     (analysis in mole %)
                 cpx Na0,06Ca0,63Fe''0,41Mg0,61Fe'''0,12Ti0,05Al0,41Si1,72O6
                 G = -463007,38 (J)  H = -356018,61 (J)  S = 72,38 (J/K)  V = 9,09 (cc)  Cp = 35,52 (J/K) 
           diopside clinoenstatit  hedenbergite alumino-buffo     buffonite      essenite       jadeite
              -6,76         31,38         41,26         16,54         -7,09         18,89          5,77

clinopyroxene    mass = 14,56 (gm)  density = 3,42 (gm/cc)     (analysis in mole %)
                 cpx Na0,03Ca0,32Fe''0,62Mg0,79Fe'''0,09Ti0,02Al0,35Si1,77O6
                 G = -212375,73 (J)  H = -161371,57 (J)  S = 34,51 (J/K)  V = 4,25 (cc)  Cp = 16,95 (J/K) 
           diopside clinoenstatit  hedenbergite alumino-buffo     buffonite      essenite       jadeite
             -53,03         64,95         62,06         13,29         -9,29         18,66          3,35

feldspar         mass = 26,90 (gm)  density = 2,65 (gm/cc)     (analysis in mole %)
                 K0,00Na0,47Ca0,53Al1,53Si2,47O8
                 G = -459947,06 (J)  H = -361093,18 (J)  S = 66,88 (J/K)  V = 10,14 (cc)  Cp = 33,22 (J/K) 
             albite     anorthite      sanidine
              46,73         53,27          0,00

Total solids     mass = 72,31 (gm)  density = 3,08 (gm/cc)
                 G = -1135330,17 (J)  H = -878483,36 (J)  S = 173,76 (J/K)  V = 23,49 (cc)  Cp = 85,69 (J/K) 

Viscosity of the System cannot be computed.

System           mass = 100,26 (gm)  density = 3,08 (gm/cc)
                 G = -1523662,30 (J)  H = -1159462,28 (J)  S = 246,39 (J/K)  V = 32,54 (cc)  Cp = 124,11 (J/K) 

Oxygen           delta moles = 0,00145398  delta grams = 0,0465258
                 G = -495,59 (J)  H = 57,85 (J)  S = 0,37 (J/K)  V = 178,69 (cc)  Cp = 0,05 (J/K) 

[asimow]

Dear Anna,

Negative values of end-members is normal and not a matter of concern. You should only be concerned if the quantity of some actual element were negative. Let's look at why you get negative end-members so you can understand my answer. The pyroxene components are:

diopside                CaMgSi2O6
clinoenstatite        Mg2Si2O6
hedenbergite        Ca(Fe2+)Si2O6
alumino-buffonite  Ca(Ti0.5Mg0.5)(AlSi)O6
buffonite              Ca(Ti0.5Mg0.5)(Si(Fe3+))O6
essenite               CaFe3+SiAlO6
jadeite                 NaAlSi2O6

So, for starters, consider how to make the perfectly legal and legitimate pyroxene ferrosilite, (Fe2+)2Si2O6. It isn't one of the end-members, but you can make it by a linear combination of them: ferrosilite = clinoenstatite + 2 hedenbergite ââ,¬â€œ 2 diopside. So that means, in normalized percent terms, ferrosilite is

diopside clinoenstatit  hedenbergite alumino-buffo     buffonite      essenite       jadeite
    -200              100               200                   0                0                0               0

In general, any low-Ca, high-Fe2+ pyroxene is going to have negative diopside (geometrically, this happens if it plots below the diagonal from enstatite to hedenbergite in the pyroxene quadrilateral and so is outside the enstatite-hedenbergite-diopside triangle).

For the non-quadrilateral components, you will note that Al-Bf has Al and Ti. Bf has Fe3+ and Ti. Ess has Al and Fe3+. By linear combinations of these three, you can make whatever amount of Al, Ti, and Fe3+ you need. But the abundances of the end-members may well be negative. Consider a pyroxene that contains tetrahedral Al but is free of either Ti or Fe3+. To make that, you have to have positive Al-Bf and Ess and negative Bf (to cancel out the Ti and Fe3+ that come along with the Al in Al-Bf and Ess).

Hope that helps!

-- Paul