GEOPHYSICAL RESEARCH LETTERS, VOL. 1 1 , NO. 10, PAGES 955-958, OCTOBER 1984
THE ECLOGITE TO GARNETITE TRANSITION
-- EXPERIMENTAL
AND THERYODYNAMIC CONSTRAINTS
Craig R. Bina and Bernard 3. Wood
Department of Geological Sciences, Northwestern University
Abstract. We have found that the forms of the
experimentally determined phase diagrams for
pyroxene-garnet
transformations require the
volume changes for these reactions to be much
smaller at 130 kbar (400 km) than at 1 atm.
Using these .volume data we calculated the width
of the eclogite-garnetite transition in natural
quartz tholeiite and alkali olivine basalt compositions taking account of mixing in multicomponent pyroxene and garnet phases. We find that
the eclogite-garnetite transition does not exhibit any discontinuity in bulk sound velocity in
the pressure range 110 to 230 kbar. In addition,
this velocity, when plotted as a function of
pressure, possesses a curvature which is in the
opposite sense to that given by the Preliminary
Reference Earth Model (PREM). This phase transition, therefore, does not appear to be a satisfactory model for the 400 km seismic discontinuity.
Introduction
The eclogite-garnetite transition has been
proposed as a possible model for the 400 km
seismic discontinuity [Anderson, 1982, 19841.
This proposition was based, in part, on the
experimental study of Akaogi and Akimoto (1977)
who found, in synthesis experiments, that pyroxene components dissolve substantially into the
garnet
structure
in the pressure range of
interest. We have taken the eclogite-garnetite
hypothesis one
step further by determining
whether the experimental data actually require a
seismic discontinuity to be produced by the
transformation of pyroxene to garnet structure in
natural eclogitic compositions. By making use of
available thermodynamic data for low pressure
mineral phases [Wood and Holloway, 1982, 19841,
we derived thermodynamic parameters for high
pressure ma jorites (pyroxene in garnet structure)
from the experimental phase equilibrium data in
the manner discussed below. We then used these
data to compute stable phase assemblages and
their properties as functions of pressure, temperature, and bulk composition by the technique
of free energy minimization.
Fe9 Sir01 2 [Akaogi and Akimo to,
19771, and
Cai .jMg~.jAl2 Sis O~r-CazMgzSirOi2 [M. Akaogi, per19831 .
These
authors
sonal communication,
obtained, in synthesis experiments, the approximate limits of majorite solution for garnet coexis ting with
pyroxene over
the pressuretemperature range of 40 to 200 kbar and 850 to
1450~~.
The coexistence of pyroxene and garnet may be
considered in terms of equilibria such as:
M4Si4012
pyroxene
=
H4Si4012
garnet
(1)
for which we have at equilibrium:
is the standard state free energy
where AGO
change
the pressure and temperature of
interest and K is the equilibrium constant.
Ex ressing K in terms of activity and referring
8 to 1 atmosphere measurements, we have
AGp,T
where H, S and V refer to enthalpy, entropy and
volume, respectively, and a4 is the activity of j
(= ~4Si4012) component in' the i phase.
The
entropies of the majorite components were calculated from known values for the aluminosilicate
garnets which were adjusted for the removal of
~ 1 and
~ the
1 addition ofI'fM
and SiVI (Table 1).
Heat capacities were estimated in the same manner
as the entropies. The activities of MsSibOIZ
components were calculated by assuming ideal
disordered (M-Si-A11 solution for the Mg- and
Fe-majorites and by applying the non-ideality
relations of Haselton and Newton (1980) for the
CaMg-majorite.
Thus, from equation (31, the
shape of the pyroxene-majorite equilibrium curve
(i.e., the pyroxene-garnet miscibility gap) on an
isothermal pressure-composition diagram (Figure
lA) is completely determined by the integral of
the volume change of reaction over the pressure
Data Base
interval of interest. The end-member (pure
M I + S ~ I +in
O ~garnet
~
structure) intercept pressure
The eclogite-garnetite transition, if
it
of the curve is determined by the standard
occurs in the earth, takes place by progressive
enthalpy change of reaction.
dissolution of M4Si4012 pyroxene (M = Mg, Fe and
To determine the functional form of AV; versus
Ca) in M3A12Si3012 garnet with increasing pressure. This gives rise to an M~A12SisO~2-MrSisO~r P, we have used the thermal expansion data of
Kieffer (1980), zero-pressure volumes from Akaogi
garnet-majorite solid solution. High pressure
and Akimoto (1977) and the review paper of Jeanphase equilibrium data are available for the
loz and Thompson (19831, and bulk modulus data
Mg3A12Si3012-Mg4Si4012, FesA12Sis 012joins
from Jeanloz (19811, Jeanloz and Thompson (19831,
and Levien et al. (1979). Gruneisen ratios and
Copyright 1984 by American Geophysical Union.
Anderson-Gruneisen parameters were obtained from
Jeanloz and Thompson (1983) and Anderson et al.
Paper number 4L6300.
(1968).
(See Table 1.) The pressure dependence
0094-8276/84/004L-6300$03.00
Bina and Wood:
TABLE 1.
Eclogite to Garnetite
Adjusted d a t a b a s e c o n s i s t e n t w i t h phase e q u i l i b r i a
PX
PX
PX
gt
gt
94.17
109.94
96 .O
189.13
224.26
a. x l o 6 ( K - ~ )
22.031
29.3
21.013
15.439
10.303
( g ) p x 1 ~ 6 :K-')
0.010
0.013
62.58
65.96
122.17
84.-112.
unknown
phase
s?OOOK
'0,298
(ca
)
raw
'0s
{ ad j .
104.-112.
106.
gt
-.
( 9 7 C6/
-%+be
14.67
0.013
104.
215.
unknown
4.5
1.1
6.3
-337 97.
Phases a r e pyroxene ( p x ) and m a j o r i t e ( g t ) . S(toOoK i s e n t r o p y a t 1000 K , a.
thermal
e x p a n s i o n e x t r a p o l a t e d t o 0 K , V o 298 z e r o - p r e s s u r e volume a t 298 K , KOS z e r o - p r e s s u r e
a d i a b a t i c b u l k modulus a t 300 K , y & r u n e i s e n r a t i o , 6 s Anderson-Gruneisen p a r a m e t e r ,
~
( e n t h1 a l p y ~ of f o ~r m a t i o~n from~ o x i d e s a t 1000 K and 1 b a r . Observed r a n g e s (raw) and
b e s t - f i t v a l u e s ( a d j . ) a r e g i v e n f o r b u l k moduli and t h e i r p r e s s u r e d e r i v a t i v e s . See t e x t
f o r references.
of t h e volume was c a l c u l a t e d using t h e secondo r d e r Birch-Murnaghan e q u a t i o n of s t a t e . Adopt i o n of a v e r a g e v a l u e s of t h e s e parameters l e a d s
t o a v e r y poor f i t t o t h e phase e q u i l i b r i u m d a t a
( F i g u r e U). However, by a d j u s t i n g t h e b u l k
m d u l i and t h e i r p r e s s u r e d e r i v a t i v e s (and, t o a
l e s s e r e x t e n t , t h e z e r o - p r e s s u r e volumes) o f t h e
g a r n e t s and pyroxenes w i t h i n t h e i r e x p e r i m e n t a l
u n c e r t a i n t i e s , we a r e a b l e t o o b t a i n a f u n c t i o n a l
form of t h e volume change of r e a c t i o n which produces an e x c e l l e n t f i t t o t h e e x p e r i m e n t a l d a t a
These b e s t - f i t v a l u e s f a l l w i t h i n
( F i g u r e LA).
t h e s c a t t e r of r e p o r t e d v a l u e s (Table 1 ) and were
o b t a i n e d by i n t e r d e p e n d e n t p e r t u r b a t i o n o f t h e
mean r e p o r t e d v a l u e s . S i n c e t h e d e r i v e d pyroxene
and m a j o r i t e p r o p e r t i e s a r e i n t e r d e p e n d e n t , we do
n o t c l a i m t h a t o u r v a l u e s a r e t h e most a c c u r a t e ;
they simply y i e l d volumes which a r e c o n s i s t e n t
w i t h t h e phase e q u i l i b r i u m d a t a .
We f i n d t h a t
t h e phase e q u i l i b r i u m d a t a r e q u i r e a volume
change of r e a c t i o n which i s s i g n i f i c a n t l y s m a l l e r
a t high p r e s s u r e s ( a p p r o x i m a t e l y 50% s m a l l e r a t
100 k b a r ) t h a n t h e z e r o - p r e s s u r e volume change
( F i g u r e 1 ~ ) ; t h i s i s t h e c a s e f o r a l l t h r e e of
the compositional joins studied.
Utilizing a
volume change which does n o t d e c r e a s e s i g n i f i c a n t l y w i t h p r e s s u r e produces a curve whose s l o p e
i s much s h a l l o w e r t h a n any curve c o n s i s t e n t w i t h
t h e e x p e r i m e n t a l d a t a ( F i g u r e lA,B). I f we were
t o assume non-ideal mixing behavior o r s h o r t
range o r d e r i n g of M ( = Mg i n t h i s c a s e ) , S i , and
A1 i n t h e m a j o r i t e - g a r n e t s o l u t i o n s , t h e c a l c u l a t e d c u r v e would be even f l a t t e r t h a n t h a t
o b t a i n e d from t h e i d e a l assumption. ( I n g e n e r a l ,
coupled s u b s t i t u t i o n s of t h e type under cons i d e r a t i o n l e a d t o p o s i t i v e e x c e s s e n t h a l p i e s and
19801; i t
s h o r t r a n g e o r d e r [ e . g . , Wood e t a l . ,
can r e a d i l y be shown t h a t t h i s l e a d s t o a s h a l lower s l o p e . Thus, t h e e x p e r i m e n t a l d a t a cons t r a i n t h e volume changes t o be v e r y s m a l l a t
h i g h p r e s s u r e s ( F i g u r e lA,B).
CALCULATED EQUILIBRIA
(A> 200
---
150
l0OO0C
-yo
,
loo
-
,
,'&
,
LII
W
C
2;
R A W FIT
-
3
01
1
1
1
...
0
ADJ
FIT
-
-/*
C
50
GT
-
o GT ( f P X )
-3
-
GT f PX
GT Conp
I
0
M~,AI,sI,o,, 20
I
I
40
60
80 M~,SI,O,,
MOLE YO
Mg,St,O
(B)
I
I
t2
I
1
loOoaC
34
1
I
0
50
I
I
100
150
PRESSURE (kb)
I
200
Fig. 1.
[A] I s o t h e r m a l
pressure-composition
diagram showing e x p e r i m e n t a l d a t a o f Akaogi and
miscibility
Akimoto (1977) and pyroxene-garnet
gap f i t t o i n i t i a l (RAW) and a d j u s t e d (ADJ.) d a t a
base.
[B] I s o t h e r m a l volume-pressure
diagram
showing volume change of p y r o x e n e - m a j o r i t e (PXGT) r e a c t i o n a s a f u n c t i o n of p r e s s u r e f o r i n i t i a l (RAW) and a d j u s t e d (ADJ.) d a t a b a s e .
Bina and Wood: Eclogite to Garnetite
Results
Having arrived at a consistent form for
AG(P), we then solved equation (3) for a best
to the equilibrium data in a
fit value of
least squares sense. This gave us a complete set
of thermodynamic data for the pyroxene-majorite
transition consistent with phase equilibrium
experiments (Table 1). We calculated the stable
phase assemblages and mineral compositions as
functions of temperature and pressure for two
natural eclogitic compositions from Green and
Ringwood (1967): a silica-oversaturated quartz
tholeiite "A" and a silica-undersaturated alkali
olivine basalt. We used thermodynamic data for
the pyroxene and aluminosilicate garnet components from Wood and Holloway (1982, 1984) and
the majorite data discussed above. The free
energy of the system was minimized utilizing the
steepest descent algorithm of Storey and Van Zeggeren (1964). From our volume and compressibility data we were able to determine the density
and the volume-averaged bulk modulus, and hence
the bulk sound velocity $$, of each stable assem-
OH(Z~~~~
*
L
MOLAR VOLUME
QUARTZ THOLEllTE
85
2.5
G T/PX
*
I
DENSITY
Fig. 3. Schematic representation of: [A] volume
change for pyroxene-garnet transition as a function of depth for initial (RAW) and adjusted
(ADJ.) data base, [B] density as a function of
depth across the eclogite-garnetite transition
for initial (RAW) and adjusted (ADJ.) data base.
PRESSURE (kbar)
ALKALI OLIVINE BASALT
I
1
t
l
l
l
PRESSURE (kbar)
Fig. 2. Bulk sound velocity (4%) as a function
of pressure along 1600 K and 2000 K isotherms for
natural eclogite compositions and comparison with
Preliminary Reference Earth Model ( P R E M - - S O ~ ~ ~
line).
[A] Quartz Tholeiite "A".
[B] Alkali
Olivine Basalt. Vertical lines labeled 0.9, 1.7,
etc. give calculated volume ratio of garnet to
pyroxene.
blage. Along 1600 K and 2000 K isotherms, the
bulk sound velocity as a function of pressure for
the quartz tholeiite (Figure 2 . ) exhibits a sharp
discontinuity at
100-110 kbar due to the
coesite-stishovite transition [silica polymorph
data from Holm et al., 1967 and Jeanloz and
Thompson, 19831 but no discontinuity due to the
eclogite-garnetite transition. This is seen more
clearly in the
silica-undersaturated
alkali
olivine basalt (Figure 2B) which exhibits no
discontinuity at all within the 50 to 230 kbar
pressure range. The eclogite-garnetite transition takes place gradually and smoothly, and much
of the transition takes place at pressures lower
than those corresponding to 400 km (i.e., approximately 130 kbar). Note also that the sense of
the curvatufe (i.e., increasing or decreasing
slope) of 42 versus P for the transition is opposite that of the Preliminary Reference Earth
Model [Dziewonski and Anderson, 19811, although
the magnitudes of the velocities do not differ
greatly.
Conclusions
We conclude that phase equilibrium data provide a strong constraint upon the volume change
of reaction as a function of pressure for the
eclogite-garnetite transition. The available
data require the volume change to be substantially smaller at high pressures than at zero
pressure (Figure 3A). Whereas a less pressure-
Bina and Wood:
Eclogite to Garnetite
dependent volume change of r e a c t i o n would permit
t h e o c c u r r e n c e of a s h a r p pyroxene-garnet t r a n s i t i o n , t h i s form of t h e volume change r e q u i r e s a
smooth t r a n s i t i o n from pyroxene t o m a j o r i t e ( F i g u r e 3B), e x h i b i t i n g no d i s c o n t i n u i t y i n b u l k
sound v e l o c i t y o v e r t h e p r e s s u r e range 110 t o 230
k b a r and producing a c u r v a t u r e of d i v e r s u s P
which i s i n t h e o p p o s i t e s e n s e t o t h a t of PREM.
I t seems p r o b a b l e , t h e r e f o r e , t h a t t h e e c l o g i t e g a r n e t i t e t r a n s i t i o n i s n o t a s a t i s f a c t o r y model
f o r t h e 400 km s e i s m i c d i s c o n t i n u i t y . We would
be a b l e t o a s s e r t t h i s c o n c l u s i o n more s t r o n g l y
i f t h e e x p e r i m e n t a l d a t a had c o n v i n c i n g l y demons t r a t e d e q u i l i b r i u m by " r e v e r s i b i l i t y " [ F y f e ,
19601 of t h e pyroxene-garnet m i s c i b i l i t y gap.
Acknowledgements.
We would l i k e t o thank
Masaki Akaogi f o r k i n d l y p r o v i d i n g u s w i t h experimental
data
on
the
C a l . jMgl. sAlzSi3012Ca2Mg2Si,01, j o i n from h i s t h e s i s and S e t h S t e i n
f o r h e l p f u l d i s c u s s i o n s of t h e s e i s m o l o g i c a l
d a t a . T h i s m a t e r i a l i s based upon work s u p p o r t e d
under a N a t i o n a l S c i e n c e Foundation Graduate F e l lowship (C.R.B.).
References
Akaogi, M . ,
and S. Akimoto,
Pyroxene-garnet
solid-solution
equilibria
i n t h e systems
Mg4Si,012-Mg,A12Si,012
and
Fe,Si,012Fe3Al2Si,Ol2 a t h i g h p r e s s u r e s and temperat u r e s , Phys. E a r t h P l a n e t . I n t e r . , 15, 90-106,
1977.
Anderson, D. L . , Chemical composition and evolut i o n of t h e m a n t l e , i n High P r e s s u r e Research
i n Geophysics, e d i t e d by S. Akimoto and M. H.
Manghnani, pp. 301-318,
C e n t e r f o r Academic
P u b l i c a t i o n s , Tokyo, 1982.
Anderson, D. L . , The e a r t h a s a p l a n e t :
paradigms and paradoxes, S c i e n c e ,
347-355,
1984.
Anderson, 0. L., E. S c h r e i b e r , R. C. Liebermann,
and N.
Soga, Some e l a s t i c c o n s t a n t d a t a on
m i n e r a l s r e l e v a n t t o g e o p h y s i c s , Rev. G e o p h ~ s .
Space Phys. ,
491-524, 196 8.
Dziewonski, A . , and D. L. Anderson, P r e l i m i n a r y
Earth Planet.
r e f e r e n c e e a r t h model,
I n t e r . , 25, 297-356, 1981.
F y f e , W. S., Hydrothermal s y n t h e s i s and d e t e r m i n a t i o n of e q u i l i b r i u m between m i n e r a l s i n t h e
s u b s o l i d u s r e g i o n , J o u r . Geol., 68, 553-556,
1960.
-
=,
.
Green, D. H., and A. E. Ringwood, An e x p e r i m e n t a l
investigation
of
t h e gabbro t o e c l o g i t e
t r a n s f o r m a t i o n and i t s p e t r o l o g i c a l a p p. l i c a t i o n s , Geochim. & Cosmochirn.-~cta, 31. 767833, 1967.
H a s e l t o n , 8. T., and R. C. Newton, Thermodynamics
o f p y r o p e - g r o s s u l a r g a r n e t s and t h e i r s t a b i l i t i e s a t h i g h t e m p e r a t u r e s and h i g h p r e s s u r e s ,
J . Geophys. k.85, 6973-6982, 1980.
Holm, J. L . , 0 . 3 . Kleppa, and E. F. Westrum,
J r . , Thermodynamics of polymorphic transformat i o n s i n s i l i c a . Thermal p r o p e r t i e s from 5 t o
1 0 7 0 ~and
~
P-T s t a b i l i t y f i e l d s f o r c o e s i t e
and s t i s h o v i t e . Geochim. & Cosmochim. As&,
3 1 , 2289-2307, 1967.
~ e a z b z ,R., M a j o r i t e : v i b r a t i o n a l and compress i o n a l p r o p e r t i e s of a h i g h - p r e s s u r e phase, J.
Geophys. &.. , 86, 6171-6179, 1981.
J e a n l o z , B., and A. B. Thompson, Phase t r a n s i t i o n s and mantle d i s c o n t i n u i t i e s ,
Geephys. Space Phvs., 2, 51-74, 1983.
K i e f f e r , S. W., Thermodynamics and l a t t i c e v i b r a t i o n s o f m i n e r a l s : a p p l i c a t i o n t o c h a i n and
s h e e t s i l i c a t e s and o r t h o s i l i c a t e s ,
Geephys. Space Phys., l8, 862-886, 1980.
L e v i e n , L., D. 3 . Weidner, and C. T. P r e w i t t ,
E l a s t i c i t y of d i o p s i d e , Phys. Chem. M i n e r a l s ,
4, 105-113, 1979.
S t o r e y , S. H . , and F. Van Zeggeren, Computation
of chemical e q u i l i b r i u m compositions, Can. J.
42, 54-55, 1964.
Wood, B. J . , T. J . B. Holland, R. C. Newton, and
0. J . Kleppa, Thermochemistry o f j a d e i t e d i o p s i d e pyroxenes, Geochim.
Cosmochim.
, -A
44, 933-941, 1980.
Wood, B . J . , and J. R. Holloway, T h e o r e t i c a l
p r e d i c t i o n of phase r e l a t i o n s h i p s i n p l a n e t a r y
m a n t l e s , J . Geophys. R s . , 87, Supplement
A1 9-A30, 1982.
Wood, B. J . , and J . R. Holloway, A thermodynamic
model f o r s u b s o l i d u s e q u i l i b r i a i n t h e system
CaO-MgO-A1.203-SiO:!,
Geochim.
Cosmochim.
,A
48, 159-176, 1984.
-
a.
a.
m. m.,
C. R. Bina and B. J . Wood, Department of Geol o g i c a l S c i e n c e s , Northwestern U n i v e r s i t y , Evanst o n , IL 60201.
(Received J u l y 20, 1984;
s t 1984.)
a c c e p t e d ~ u ~ u 15,