Mixed oxidation states in CalcZAF

[Brian Joy]

No, I didn't post the wrong image.  The rock (the locality escapes me) contains a spinel-group mineral that ranges in composition (apparently continuously) from essentially pure magnetite to a mineral that contains in excess of 30 wt% Cr2O3.  I don’t know if the Cr-rich material has the “inverse” or “normal” spinel structure or something intermediate.  I may have used the term “magnetite” too loosely.  Regardless, the cation:oxygen ratio is still 3:4.

The only point I’m really trying to make is that there is some convenience in specifying the above ratio within the matrix correction iterations, as then the excess oxygen mass is determined automatically.

[Probeman]

No, I didn't post the wrong image.  The rock (the locality escapes me) contains a spinel-group mineral that ranges in composition (apparently continuously) from essentially pure magnetite to a mineral that contains in excess of 30 wt% Cr2O3.  I don’t know if the Cr-rich material has the “inverse” or “normal” structure.  I may have used the term “magnetite” too loosely.  Regardless, the cation:oxygen ratio is still 3:4.

The only point I’m really trying to make is that there is some convenience in specifying the above ratio within the matrix correction iterations, as then the excess oxygen mass is determined automatically.

Hi Brian,
I appreciate that the composition varies.  It's just that I asked you for an example of the *same* composition both with and without the mineral normalization adjustment of oxygen in the matrix iteration. The reason being that I suspect the effect on the matrix correction, with the expected range of change in excess oxygen, is only a few hundred PPM and therefore "in the noise".

I also appreciate that the method you propose can calculate the excess oxygen automatically for a given stoichiometry. That is very cool. But in this particular range of compositions, it would make as much sense to perform a specific mineral normalization *after* specifying oxygen by difference, by fixed composition or by fixed stoichiometry in the matrix iteration.  I suspect the change in the matrix effect in all these cases will be relatively insignificant from the mineral normalization.

But I'll grant you it's a clever idea to perform the mineral re-normalization in the matrix iteration. Though besides the apparent minimal effect of the matrix correction from this iterated mineral normalization, my other difficulty would be figuring out how to make this method of yours "universal" for all compositions and stochiometries.

It still seems like a lot of work for a small benefit, but maybe there other examples with larger matrix corrections (such as the halogen equivalence correction for F Ka in fluor-phlogopite example I have already implemented in the CalcZAF/Probe for EPMA code), that would benefit more from this treatment? Let's think about it.

Thanks for posting your thoughts and questions. I am very interested in pursuing these ideas further.

[Probeman]

Here's an example of a modification of a calculated oxygen concentration during the matrix correction due to the halogen equivalence correction.

If we analyze a fluor-phlogopite with default oxygen stochiometry we obtain something like this:

Un    4 fluor-phlogopite, Results in Oxide Weight Percents

ELEM:      MgO       F    SiO2       O   Al2O3     K2O   SUM 
   121  29.467   9.261  42.990    .000  12.100  11.180 104.998
   122  29.329   9.508  43.069    .000  12.100  11.180 105.185
   123  29.270   9.348  42.982    .000  12.100  11.180 104.879
   124  28.759   8.999  43.073    .000  12.100  11.180 104.111
   125  28.779   9.208  42.038    .000  12.100  11.180 103.305
   126  28.974   9.253  42.571    .000  12.100  11.180 104.078

AVER:   29.096   9.263  42.787    .000  12.100  11.180 104.426
SDEV:     .300    .167    .412    .000    .000    .000    .719
SERR:     .123    .068    .168    .000    .000    .000
%RSD:     1.03    1.81     .96 -154.92     .00     .00
STDS:      273     835     273     ---     ---     ---

ZCOR:   1.4193  3.6139  1.3345     ---     ---     ---


Note that the total is high and that the fluorine concentration is around 9.2 wt% when it should be 9.0 wt%.  Why is this?  Because the matrix correction for F ka is too high from the extra 3 or 4 % oxygen being added in by stoichiometry.  Note the ZCOR (matrix correction) is about 3.6.

But because fluorine is replacing some of the stoichiometric oxygen, we need to apply the halogen correction in PFE, which not only subtracts the halogen equivalent of oxygen, but re-calculates the matrix correction for fluorine as seen here iteratively:

Un    4 fluor-phlogopite, Results in Oxide Weight Percents

ELEM:      MgO       F    SiO2       O   Al2O3     K2O   SUM 
   121  29.203   9.036  43.035  -3.805  12.100  11.180 100.750
   122  29.060   9.270  43.115  -3.903  12.100  11.180 100.821
   123  29.005   9.118  43.027  -3.839  12.100  11.180 100.591
   124  28.507   8.785  43.115  -3.699  12.100  11.180  99.988
   125  28.520   8.982  42.083  -3.782  12.100  11.180  99.082
   126  28.713   9.026  42.616  -3.801  12.100  11.180  99.834

AVER:   28.835   9.036  42.832  -3.805  12.100  11.180 100.178
SDEV:     .296    .159    .412    .067    .000    .000    .673
SERR:     .121    .065    .168    .027    .000    .000
%RSD:     1.03    1.76     .96   -1.76     .00     .00
STDS:      273     835     273     ---     ---     ---

ZCOR:   1.4065  3.5254  1.3359     ---     ---     ---


Now the fluorine concentration is correct and note that the matrix correction is significantly less at 3.5.  This is because F Ka is strongly absorbed by oxygen and therefore the matrix correction needs to be calculated again.

The CalcZAF.dat example input file contains a similar sample.

[Probeman]

No, I didn't post the wrong image.  The rock (the locality escapes me) contains a spinel-group mineral that ranges in composition (apparently continuously) from essentially pure magnetite to a mineral that contains in excess of 30 wt% Cr2O3.  I don’t know if the Cr-rich material has the “inverse” or “normal” structure.  I may have used the term “magnetite” too loosely.  Regardless, the cation:oxygen ratio is still 3:4.

The only point I’m really trying to make is that there is some convenience in specifying the above ratio within the matrix correction iterations, as then the excess oxygen mass is determined automatically.

Hi Brian,
I do agree with you on the "determined automatically" aspect of this.

Even if the difference in the matrix correction between say, oxygen by difference and oxygen by 3:4 stoichiometry is insignificant in these oxides, this method of yours does allow for an independent determination of Fe charge states.

That is to say,  this method doesn't have to be in the matrix correction iteration, but it certainly doesn't hurt to have it there... I'm trying to think of how to implement this for all oxide chemistries.

[Probeman]

Can someone explain something to me (I'm no geologist!)? If chromite is FeCr2O4 to MgCr2O4 (all iron is Fe+2), why do the Smithsonian chromite compositions contain some excess oxygen?

St  396 Chromite (UC # 523-9)
Average Total Oxygen:       33.042     Average Total Weight%:  100.194
Average Calculated Oxygen:  31.942     Average Atomic Number:   17.533
Average Excess Oxygen:       1.100     Average Atomic Weight:   27.796

ELEM:    Cr2O3    TiO2   Al2O3     FeO     MnO     MgO    V2O3       O    SiO2
XRAY:      ka      ka      ka      ka      ka      ka      ka      ka      ka
OXWT:   46.632    .500  14.530  26.620    .191  10.431    .179   1.100    .011
ELWT:   31.905    .300   7.690  20.692    .148   6.290    .122  33.042    .005
KFAC:    .3060   .0031   .0469   .1836   .0013   .0330   .0011   .2290   .0000
ZCOR:   1.0427   .9632  1.6398  1.1272  1.1104  1.9040  1.0698  1.4431  1.4097
AT% :   17.023    .174   7.907  10.279    .075   7.180    .066  57.292    .005
24 O:    7.131    .073   3.312   4.306    .031   3.008    .028  24.000    .002


St  455 Chromite USNM 117075
Average Total Oxygen:       33.208     Average Total Weight%:   99.640
Average Calculated Oxygen:  32.909     Average Atomic Number:   17.187
Average Excess Oxygen:        .299     Average Atomic Weight:   27.414

ELEM:    Cr2O3     FeO   Al2O3     MgO     CaO     MnO    TiO2     NiO    SiO2       O
XRAY:      ka      ka      ka      ka      ka      ka      ka      ka      ka      ka
OXWT:   60.502  13.040   9.920  15.200    .120    .230    .120    .160    .049    .299
ELWT:   41.395  10.136   5.250   9.166    .086    .178    .072    .126    .023  33.208
KFAC:    .3859   .0890   .0317   .0493   .0009   .0016   .0008   .0011   .0002   .2384
ZCOR:   1.0727  1.1388  1.6541  1.8607   .9619  1.1152   .9396  1.1224  1.3950  1.3931
AT% :   21.903   4.993   5.353  10.376    .059    .089    .041    .059    .023  57.103
24 O:    9.206   2.099   2.250   4.361    .025    .037    .017    .025    .009  24.000


If Al2O3 replaces some Cr2O3, that won't change the cation stoichiometry, right?

[qEd]

If measured oxygen is < the calculated, how is that an excess?

[Probeman]

If measured oxygen is < the calculated, how is that an excess?

It's a "negative" excess!   

What? You can't handle negative results?   

In any case, we're not measuring oxygen, we're just calculating it by cation stoichiometry and then adjusting that oxygen concentration for various reasons, e.g., halogen equivalence, FeO/Fe2O3 ratio, etc... and then re-calculating the matrix correction for the change in stoichiometric oxygen.   

[Paul Carpenter]

Many terrestrial minerals contain both Fe2+ and Fe3+. The Smithsonian wet chemical analyses measure Fe gravimetrically to get Fe0, and also a titration is done to determine Fe 2+ vs. 3+
Phases like fayalite may contain small amounts of Fe3+
Andradite garnet by definition is an Fe3+ garnet end member, but almandine is the nominally Fe2+ end member.
Info like this is available on web mineral web pages and in mineralogy texts.

Paul

[Probeman]

Many terrestrial minerals contain both Fe2+ and Fe3+. The Smithsonian wet chemical analyses measure Fe gravimetrically to get Fe0, and also a titration is done to determine Fe 2+ vs. 3+
Phases like fayalite may contain small amounts of Fe3+
Andradite garnet by definition is an Fe3+ garnet end member, but almandine is the nominally Fe2+ end member.
Info like this is available on web mineral web pages and in mineralogy texts.

I am not explaining myself well enough. I am aware that Fe+2 and Fe+3 coexist in many minerals, but if the ideal chromite formula is FeCr2O4 to MgCr2O4, that is, all Fe is as FeO (Fe+2), then why do the Smithsonian chromite compositions contain some excess oxygen when Fe is calculated as FeO? 

I get that Al2O3 can replace Cr2O3 in the chromite formula, alright.  But that won't change the cation to oxygen ratio, correct?   I guess my question is: can we get a "chromite structure" where all the Cr is replaced by Al such that it is FeAl2O4 and all Fe is still FeO?

More specifically, where is the excess oxygen coming from?  Clearly some of the Fe is Fe+3 but which site is it going into?  The Cr2O3 site I guess?  I assume it's a structural issue.

[Julien]

Jarosewich et al 1980 report this analysis with a comment (#3: Total Fe reported as FeO). However, I agree with others that it is common for spinel-group mineral to have substitution of Al2O3 or Cr2O3 by Fe2O3. You can have a glimpse (estimate) of the FeO vs. Fe2O3 by using an oxygen AND cation normalization (i.e., you fix as a constraint both the total number of anion, 4 for chromite, and the total number of cation, 3). With this, you can perform a charge balance (how many positive charges, assuming only FeO, do you have to compensate for the 8 negative charges? If not enough positive charges, then you "convert" some FeO to Fe2O3 to balance the charge).

I've played with the chromite analysis given in Jarosewich. Here are the results (1st line = cation AND oxygen normalization, 2nd line = oxygen normalization only assuming all Fe as Fe2+):

         Al2O3   Cr2O3   Fe2O3   FeO   MgO   MnO   Total   
Cation   9.92   60.50   3.45   9.93   15.20   0.11   99.12   
Oxygen   9.92   60.50   0.00   13.04   15.20   0.11   98.77   
                        
         Al      Cr      Fe3+   Fe2+      Mg      Mn      Cation      O
Cation   0.376   1.540   0.084   0.267   0.730   0.003   3.000   4.000
Oxygen   0.380   1.556   0.000   0.355   0.737   0.003   3.032   4.000


Interestingly enough, with the estimate of Fe2+ / Fe3+, the total number of trivalent cation is now EXACTLY 2.000 (versus 1.937 if you assume all Fe2+ as Fe3+). This is EXACTLY the mineral formula of chromite:

(Fe2+ 0.267, Mg 0.730, Mn 0.003) (Cr 1.540, Al 0.376, Fe3+ 0.084) O4

Sum trivalent = 2.000
Sum divalent = 1.000

Now of course this is the CALCULATED (estimate!!!) of Fe2O3 - not measured. This addition of Fe3+ represent an excess of 0.346 wt-% oxygen, close to the 0.299 you report. Maybe the 0.299 actually reflect a non-published MEASUREMENT of Fe2O3 and FeO by Mössbauer or so...

QED.

[Julien]

Here is a summary spreadsheet of my test... I used my website to run the normalization (http://cub.geoloweb.ch/index.php?page=mineral_formula).

J.

[Probeman]

Here is a summary spreadsheet of my test... I used my website to run the normalization (http://cub.geoloweb.ch/index.php?page=mineral_formula).

J.

Thanks Julien,
That makes more sense!

FYI to all: you need to be logged in to see Julien's attachment in the above post.

[jeffchen]

I understand the purpose of recalculating the oxidation state of multi-valent elements is to satisfy the "assumed chemical formula" of a crystalline phase. In the context of high temperature metallurgy, many phases do not really have fixed "formula", an example is magnetite. At high temperature(~1450oC) in air, magnetite can take significant more Fe3+ so that Fe3+/Fe2+ in it is greater than 2. 

I'd appreciate if someone could educate me to what extent mineral phases are close to their the theoretical chemical formulas in geological context.

[Probeman]

I understand the purpose of recalculating the oxidation state of multi-valent elements is to satisfy the "assumed chemical formula" of a crystalline phase. In the context of high temperature metallurgy, many phases do not really have fixed "formula", an example is magnetite. At high temperature(~1450oC) in air, magnetite can take significant more Fe3+ so that Fe3+/Fe2+ in it is greater than 2. 

I'd appreciate if someone could educate me to what extent mineral phases are close to their the theoretical chemical formulas in geological context.

Hi Jeff,
I am not a geologist so I probably can't help you, but I have a question.  Are you saying, for example, that in the case of magnetite Fe3O4, which is ideally composed of one FeO molecule and one Fe2O3 molecule, that at high temperatures, the ratio of FeO to Fe2O3 is no longer 1:1?  That there are more Fe2O3 molecules than FeO molecules in high temperature magnetite?
john

[jon_wade]

Bernie Wood, a long time ago, wrote a paper on spinels (I believe) and noted that because the Fe substitution mechanism is known, analysing those elements that Fe 3+ can substitute in for allows you to accurately determine the speciation of iron, with accuracy approaching Mössbauer.  Yeah, yeah accurate standards of known Fe2/3+ are required and good probe stats required (Peaksight 6 defeated me last time I attempted this - it had count times the stopped at a fixed precision, now changed I believe), but it works. 

The reason I was interested is trying to do Fe speciation by XANES in crystalline materials is a weapons grade pain in the posterior and a drain on life force.  Sometimes the old skool probe is just better.