Uncertainties in the calculated P-T projection

Chapter 1: Chapter 1: Introduction

L. L Introduction

L.3 Calculated phase relations in amphibolites

2.5 Uncertainties in the calculated P-T projection

The internally consistent nature of the data used to calculate the phase diag¡am (Fig.

2.3) allows some confidence in the predictions of these diagrams (especially in the relative positions of the stability fields ^and the slopes of the univariant reactions which separate them).

However, there are

still

substantial uncertainties

in

the data themselves and these may have a

significant effect on rhe loci of the equilibria in P-T space. For example, the ^slopes of most

of

the reactions involved in the mid-pressure, mid-temperature invariant points,

[Grt]

^and

[Chl]'

are

fairly

similar and their sub-parallel

natue

means that the positions

of [Grt]

^and [Chl], marked by the intersection of these univariants,

will

not be

well

defined. However, both

of

these bundles of reactions also involve the near-perpendicular reaction;

orthoamphibole + sillimanite

=

staurolite +

cordierite ^(Grt'

^Chl)'

The high angle at which this reaction intersects the other reactions ^means that

it

effectively controls the position

of

both of the inva¡iant

points. It follows

that any error in the position

of

the reaction (Grt, Chl) may have a considerable effect on the absolute position of the critical assemblages

in

P-T space.

Although many of the data required for equilibrium thermodynamics calculations ^are relatively

well

characterised from experimental

work,

standa¡d molal enthalpies of formation are notoriously

difficult

to determine to ^an acceptable level of accuracy (llelgeson et al., 1978;

Powell

&

Holland. 1985). The ur¡certainties on standard molal enthalpies of formation determined from both molten ^salt calorimetry and

low

temperature heat by solution in

IIF

are

high and may cause errors

in

the calculated position

of

a reaction of as much as 100"C

(Helgeson er al., 1973). For this reason

it

is assumed that the enthalpy ^data of the mineral end members

will

be the major contributors to uncertainties

in

the P-T conditions of the calculated mineral equilibria.

The uncertainties on the thermodynamic data used in the calculation of Fig' 2,3 a¡e listed in Appendix

A2.

Although the aluminosilicates, quartz and water vapour all have

fairly

insignificant uncertainties on AH¡, and those for the end members clinochlore, aÍnesite,

almandineandpyropearealsoquitelow (3.21,2.98,2.78,2.33kJ mol'lrespectively),the

uncertainties

for

the enthalpies of formation of the other end-members ^are comparatively high' The most uncertain data

ue

^those for Mg-staurolite, Fe-staurolite , gedrite,ferro-anthophyllite

Chaptcr2-FMASII-

¹⁶

and anthophytlíte (8.31, 8.17, 6.55, 6.44, 5.58 kJ

mol-l respectively). It

is unfortunate that the reaction

conrolling

^{the position of both}

[chl]

^and [Grt] involves ^phases

with

signif,rcant uncertainties. Figure 2.4 illustrates the uncertainry

in

the P-T position of the invariant point

[chl]

^{due to} altering the

ñI

^{of gedrite and both}

^Fe-

^and Mg-staurolir¿ wirhin the limits of their uncertainties.

Another source of potential problems in the calculated equilibria is in the relative Fe-Mg partitioning exhibited by staurolite and garnet which, in natural rocks, may have overlapping Xps ^(see section

2.2).

Small ^changes in the enthalpy of one

of

the staurolite end members (or

in

the thermodynamic data or a-X (activiry-composition) relations of garnet) may cause ^an exaggeration (or, ^less

likely,

^a reversal) of the differences in the calculated compositions

of

staurolite or garnet.

2.6

^comparison

between ^obserYed and calculated ^phase relations in aluminous ^schists

The positions

of

the invariant points in the calculated P-T projection

(Fig'

2'3)

correspond quite

well with

the relative positions of the real assemblages in P-T space and wittt theestimatedtemperaturesof

equilibrationof

theserocks (seesections2'3

&'2'4)' ^T\e

calculated pressures of the inva¡iant points in Fig. 2.3 also ^seem to correspond reasonably well

with

the information ^obtained from the natural rocks, however the ^presence of additional components is

likely

to have ^a significant effect on this conformity'

Most natural aluminous ^schists contain ^at least ^a small proportion of plagioclase' ^a titanium phase and sometimes ^a small amount of biotite ^(e'g'

Harley'

1985;

Arnold &

sandiford,

1990). While

rutile

^(or ilmenite), biotite and anorthite ^are each stabilised by ^an additional component which is not easily incorporated into other phases, albite is stabilised by the presence

of

sodium which may also be partitioned into the strucn¡re of orthoamphiboles.

This means that

for

nearly a// natural examples, the phase relations in aluminous schists ^are mofe properly ^described

in

the

NFMASH

rather than the

FMASH

^system'

If

the ^phase diagram is projected from plagioclase ^(as

it

is effectiveiy for the other additional components'

K

and

Ti)

then the orthoamphibole-bearing assemblages

will

be stabilised with respect to the orher phases and those stability fieids

will

be expanded along (down) the [Oam] reactions' Because

it

is

the

modelsysrem

FMASH

^{which is} of primary interest here (a system which ^can later be ^used to explain the effects of minor additional components ^{such as} Na)' the calculated

equilibria

^{in Fig.2.3 are} considered to occur ai excessively

low

pfessures'

of

most

significance is the likelihood that

with

the addition

of

Na to the ^phase diagram in

Fig' 2'3'the

invariant point Ip1 is

likely

to move to lower pressures, thus allowing orthoamphiboie to ^be

stable

with

andalusite and thus contradicting the observed ^phase relations'

As mentioned previously, the uncertainties

in

the thermodynamic data used ^to calculate the P-T projection in Fig.

2.3

¿requite considerable, especially

for

the mst' _fst' ^ged'

fath

^and

anth

endmembers. Therefore it is possible to adjust the

aH

data for these endmember ^phases without invalidating the results of the calculations. ^Because

of

the old ^and inaccurate nature

of

ChaPter2-FMASll-

¹⁷

7

6

(ú

-o l¿

o-

5

600

2.4. The

to 20 kJmol-l

650

T ("C)

700 750

Figure from 0

[Chl] ^{or Ip1,} with irrcreasing ÂHr"a 5 kJmol-l ^(squares).

-15

-14 -12

-10 10

I

-8 6 -6

4 -4 Ky

2 siil -2

0

20 18

16 14 12

Chapter2-t;MASII-

^I8

the thermodynamic ^data

for

rhe gedriteend.member which was ^generated from the experimenral data

of

Schreyer and Seifert (1969b; ^see also

Howell,

1991), altering the enthalpy of gedrite is considered to be the most appropriate adjusunent to make to ^the data

set'

^In order to bener represent the ^phase relations in the

FMASH

model system, ^the enthalpy ^o1 gedrite ^{(^HguÐ}

should be altered by ^a factor which places Ip1 high up

in

the sillimanite stability

field

^(Howell, 1991;

Xu

et al., 1993). For rocks containing sodium, Ip1 may then move down pressure' along the

[oam] FMASH

univariantreaction, without leaving the sillimanite stability freld'

2.7FMr1isHgridwithadjustedthermodynamicdata

AsecondP-Tprojection(Fig2.5)hasbeencalculatedfortheFMAsHsystem(with

qJarïzand aqueous vapour in excess)

involving

aluminosilicates, staurolite' cordierite' ^gafnet' chlorite and. orthoamphibole, using ^the pennanent datafile in Appendix A3 in

with

the enthalpy of ged,rite

lnfqd

^{adjusted by}

⁺

¹⁰

^kJmol-l'