The effect of uncertainties in the data and activity models

CFMASH +An,Qtz,HzO

3.5.3 The effect of uncertainties in the data and activity models

As discussed

previously,low

^variance assemblages from natural amphibolites ^suggest that the ^phase diagram

for

amphibolites is

likely

to involve the three invariant points

represented

in Fig.

3.4 (i.e.

[chl, Hbl], [chl,crd],

^and

[chl, Grt])

^{and possibly also [Als,}

chll

or [St,Chl] which ^contrasts

with

the calculations summarised in Fig.

3.7.

^{Since the}

discrepancy ^appears unlikely to be due to the effects of additional minor components or

reduced agr6,

it

seems

likely

that ^some of the thermodynamic data may ^be in

error'

^{Note that a} similar conclusion was reached by

Howell

(1991) and also by

Xu

(1994) who made

adjustments to the enthalpy value

for

end-membet

gedritelntheFMAsH

^{system until the}

calculated ^phase relations matched ^those known from petrological observation.

In the case of the chlorite-bearing, orthoamphibole ^absent CFMASH model system, the least

well

consüained thermodynamic data ^{are those} for the end-members, Fe-staurolite' Mg- staurolite , tremolite,

Fe+remolite

^and hornblende ^(see Appendix

A2).

Another factor which

ChaPter3-CFMASH- ⁴⁶

tr

x il-¡

_I

_¡

"x x- Þ

a

X

x

x

^a

0.9 0.8 0.7 0.6

s

^0.5

X

0.3 0.2 0.1 0

rH o

^Selv

.L O ^RAJ

^ ^S&R À ^F&H X

^SPear

xs

o 0.05 o.1o 0.15 0'20 0.25 o'30 o'35 o'40 0'45

^0'50

XFeg*,Mz

Chaprcr3-Ct;MASII-

⁴⁷

may cause problems in the calculations is departure in the real minerals from the a-X relations assumed in formulating the data and ^the permanent datafiles. The most

likely

sources of such discrepancies ^are

in

the mixing of end-members in which some of the cations are

of

significantly different size. For example, garnet

in

the

CFMASH

^{system has been considered} to be an ideal solid solution of pyrope, almandine and

grossular.

However, given the

differences in the size of calcium, iron and magnesium ions, mixing beween these end- members is

likely

to be non-ideal.

In

the case of the aluminous chlorite endmember, ^arnesite, the experiments used to derive the thermodynamic ^data were ^based on solid-solution chlorite which did not closely approach ^the amesite endmember. Thus the thermodynamic ^{data are} strongly dependent on the (possibly suspect) activity model used to derive them (R. Powell, pers. comm

.,1993).

The effect of the non-ideality

of

a-X relations

in

garnet, and

of

adjusting the thermodynamic data

within

error for the ^less

well

constrained end-members, are discussed below.

Garnet

Non-ideality of mixing ^{may be} modelled using activity coefficients which relate the activity of the ideal end-member to that of its non-ideal, more realistic counterpart (Powell, 1971;Wood

&

Fraser,

1984).

^{(See Appendix}

44,

section A4.3.2

for

the formulation

of

activity-composition (a-X) relations for TI{ERMOCALC permanent data

frles.) Activity

coefficients

(ï)

are a function of the composition of the phase (RT/n Y= wAij

/(X)

where wA¡i are interaction parameters

for

the mixing of the end-members

i

^and

j

in the phase

A).

Powell (pers. comm., 1gg3) has suggested two models for non-ideality

in

the mixing relations

of

pyrope, almand.íne ^and grossular

in

gamet (R. Powell, pers. comm.,1993); one for Ca-rich

and the other for low-Ca garnets. The garnets of interest in hornblende-staurolite amphibolites typically

fall in

the low-Ca region where the interaction parameters have determined ^as:

wGrtF.Mg

=

^190R

=

^{1.6 kJ}

K-l

wGtrcaFe - wGrrcaMg = ^-1100R = ^-9.1 kJ

K-l

(R. Powell, pers. comm.,

1993). A

range of values

for

wGttcaFe ând wGrtaaMg were used to formulate activiry models of garnet and the effects of these are illustrated in Fig. 3-12.

Fot

significant non-ideality

in

garnet (i.e. large interaction pammeters e.g. wcrtçaFe = ⁵ kJ K-1 and wG.tcuMs

= l4.I

kJ K-1), the

CFMASH

invariants

[Hbl,

^{Oam] and} [Chl, Oam] ^{move a} signif,rcant distance toward [Grt, ^Oam],

implying

that non-ideality

in

^garnet activity-

composition (a-X) relations may ^be part of the reason for the difficulties encountered in the chlorite-bearing

CFMASH grid.

However, the effect

of

the non-ideality

in

garnet is insufficient to allow the predicted phase relations to corespond with those observed petrologically.

Chapter3-CFMASH- ⁴⁸

[Crd]

[Als]

I I

. ^original I

i

adjusted staurolite

tstl tGrtl

/

tchll

o /

lHbll

10

I

I

7

L(ú

-ol¿

o-

6

5

550 600

650

⁷⁰⁰

T

^("C)

Chapter3-CFMASII- ⁴⁹

Chlorite

Although the ideal mixing model assumed in the derivation of the thermodynamic ^data of amesite is probably an over-simplif,rcation, ^the resulting data ^are strongly dependent on the

activity

^{model used to} derive them (R. Powell, pers. comm',

1993)'

Thus, the uncertainry associated

with

the enthalpy of amesite is probably larger than the listed

sd(fl)

^{(see Appendix}

A3).

To determine whether the assumption of the ideal mixing allows sufficiently uncertainty to cause ^an inversion

of

the ^phase diagram topology, the enthalpy of amesite (AII¡ttss) was varied

within

the furl range of its 2o error bar (+6 kJ

mol-l).

^{This caused all of the}

^CFMASH

invariant points

involving

chlorite to move toward the

[Chl]

inva¡iant (which ^as

it

^{does not}

involve

the end-me ^mber arnesire, obviously is not affected by ^changes in the data for amesite),

(Fig.

3.12).

The degree of movement experienced by each of the invariant points ^ÀFla¡¡ss wâs slight and certainly insufficient ^{to cause an} inversion of the topology'

Hornblende

The enthalpy of the hornblende end-members hornblende, nemolite ^and Fe-tremoiite are associate

with

considerable uncertainties (sd

(II)

₌ 4'55,

5'08

^{anð' 6'25 kJ}

mol-l

respectively, ^see Appendix

A2)

which could be partly responsible for the inadequacies of the calculated ^phase diagram. The effect of varying the enthalpy of either harnblende or both

tremolite

^and,

Fe-trennlite

tothe

full

extent of thei¡ uncertainties is to ^cause the stable and metastable

CFMASH

^invariant points to converge, however, the shifts ^are insufficient to cause an inversion

of

topology (Fig. 3.13).

Staurolite

The targe uncertainties in the enthalpy values

for

the stauolite end-members suggest that staurolite may be ^a potential ^source for the inadequacies of the calculated chlorite-bearing grid (see Appendix

A2). If

the least

well

defined enthalpy, ^ÀH¡5¡, is adjusted to the

full

extent

of

its uncertainty (by aHrst = ^{-17 kJ}

mol-l)

^{the GFMASH} invariant points draw very close together (Fig.

3.12).

However, in doing ^so, the predicted compositions of the ^phases became unrealistic,

with

staurolite calculated ^as significantly more Fe-rich than garnet'

A

more

satisfactory result was obtained by adjusting ^AFI¡5¡ and AH¡¡3¡ by equal' smaller amounts (e'g' aH¡5¡, ^aH¡¡15¡ =

-

15 kJ

mol-l).

^This adjustment allows the topology

of

the calculated phase diagram to invert so that the [Hbl, Oam] ^{and [St,} Oam] CFMASH invariant points become metastable

with

respect to the remaining orthoamphibole-absent points, [Chl,

Oam]'

[Crd'

Oam], [Als, oam],

[Grt,

oam]

^(Fig.

^3.1a).

This topology would ^then allow the

orthoamphibole-bea¡ing invariant points [Crd,

Chl],

_[Grt,

Chl]

and

[Hbl' ^Chl]

to be stable' in agreement

with

the phase relations determined from natural rocks.

Chapter3-CFMASII- ⁵⁰

lAlsl

. ^original

r

_AHrru

_{= -10 kJ}

mol-1

o

AHtr

-

^ÂH1,

= -10 kJ

mol'1

tsrl lGrtl

tchrl

\ -\

a lHbrl

10

I

I

7

L(d

-ol¿

È

6

5

550

600 650 700

T ^("C)

Fisure 3.13. The effects of ^the uncertainty in the enthalpy ^o-f hornblende ÂH¡5 = ^-19

¡¡

ilå,Ïi";ä'od:Ïü* i-rol ^Ü

^{*"r_r õn the} rocationïof ^the orthoamphibole-absent CFMASH univariant _Points.

Chapter3-CFMASII- 51

10

I

(Ú

-o l¿

fL

8

7

6

600 650 700 750

T ^("C)

(s0 CFMASH

+An,Qtz,HzO

a

o?

,ã (st)

z _q t

C,fl gtÀn lCrdl

sill

(Hbr)

%

7c oé

lchll

Hzo lGrtl

o4

[Als]

õ

o' o^IJ

c Eo

g)

oô.¡

I o ('

F

Hbl,

An)(Hbl)

^{(S0 (Hbr)}

Chapter3-CFMASII- ⁵²