Effect of jadeite component on the paragenesis of eclogitic rocks

EARTH AND PLANETARY SCIENCE LETTERS 2 (1967) 249-254. NORTH-HOLLAND PUBL. COMP., AMSTERDAM

EFFECT OF JADEITE COMPONENT ON THE PARAGENESIS OF ECLOGITIC ROCKS Shohei BANNO *

Geological Institute, University of Tokyo. Tokyo, Japan Received 2 M a y 1967

On the b a s i s of an analysis of the p a r a g e n e t i c relationships in a simple hypothetical system, a gene r a l relationship between the jadeite component in omphacite and the g r o s s u l a r component in garnet in eclogitic rocks, is presented. It is concluded that in eclogitic rocks an i n c r e a s i n g amount of jadeite in omphacite is accompanied by a d e c r e a s e in the g r o s s u l a r content of garnet, whereas in grosspydite the relationship is r e v e r s e d . This relationship is applied to the i n t e r p r e t a t i o n of the p a r a g e n e s i s of natural eclogitic rocks.

1. I N T R O D U C T I O N In c o m p a r i n g t h e p a r a g e n e s i s of e c l o g i t e , f r e q u e n t u s e i s m a d e of t h e A C F d i a g r a m , b a s e d o n t h e r a t i o (A1203 + F e 2 0 3 ) - ( N a 2 0 + K 2 0 ) : C a O : (MgO + F e O ) . T h e p l o t t i n g of o m p h a c i t e on t h i s diagram assumes t h a t t h e e f f e c t s of a l k a l i - p y r o x e n e c o m p o n e n t s i n c l i n o p y r o x e n e a n d t h a t of Mg-Fe substitution in both clinopyroxene and g a r n e t , a r e n e g l i g i b l e in d e t e r m i n i n g t h e c o m p o s i t i o n a l r a n g e i n r e g a r d to A1, Ca, M g a n d F e . In a s i m p l e way, d i s c u s s i o n s of M g - F e p a r t i t i o n between garnet and clinopyroxene may justifiably ignore the alkali-pyroxene components, but only if m i x i n g of t h e a l k a l i - p y r o x e n e c o m p o n e n t s w i t h diopside and hedenbergite components is regarded as ideal. In a d e t a i l e d d i s c u s s i o n of t h e c o m p o s i t i o n a l r a n g e of t h e c o n s t i t u e n t s of e c l o g i t e a n d g a r n e t p e r i d o t i t e , h o w e v e r , t h e e f f e c t s of a l k a l i - p y r o x erie c o m p o n e n t s a n d of M g - F e s u b s t i t u t i o n a r e s o m e t i m e s not n e g l i g i b l e . Sobolev, Z i u z i n a n d K u z n e t s o v a [1] h a v e shown that there is an intimate relation between t h e N a 2 0 c o n t e n t of o m p h a c i t e a n d t h e C a / ( C a + M g + F e 2+) r a t i o of g a r n e t i n g r o s s p y d i t e a n d associated eclogite xenoliths in the Zagodochnaya pipe, Yakutia. Their diagram is reproduced in fig. 1 (full l i n e ) . T h i s r e l a t i o n w i l l b e r e f e r r e d to h e r e i n a s S o b o l e v ' s r u l e . T h e p o t e n t i a l ( c h e m -

* T e m p o r a r y a d d r e s s : D e p a r t m e n t of Geophysics and Geochemistry, Australian National University, Canb e r r a , Australia.

i c a l ) of N a 2 0 w a s c o n s i d e r e d b y S o b o l e v e t al. a s the essential factor controlling this relation. In t h i s p a p e r , t h e r o l e of a l k a l i - p y r o x e n e c o m p o n e n t s in t h e c l i n o p y r o x e n e - g a r n e t paragenesis will be discussed for some simplified s y s t e m s a n d t h e r e s u l t s w i l l b e a p p l i e d to t h e i n t e r p r e t a t i o n of n a t u r a l a s s e m b l a g e s . T h e a l k a l i pyroxene component will be represented by jadeite. T h e e f f e c t of M g - F e s u b s t i t u t i o n o n t h e c o r n -

90

70

÷

50 ,%

u 30

Fig. 1. The r e l a t i o n between C a / ( C a + M g + F e ) o f g a r net and Na20 content of omphacite from grosspydites and kyanite eclogites [1]. The straight lines a r e a f t e r Sobolev et al. [I] and the broken line is by the author.

250

S. BANNO AI2o~

FT .~.¢.

CaSiO~

/Ill

GAR

MgSi03

D~OPSIDE

Fig. 2. A schematic r e p r e s e n t a t i o n of a hypothetical equilibrium relationship in the system A1203-CaSiO3-MgSiO 3. p o s i t i o n of p y r o x e n e s a s s o c i a t e d w i t h g a r n e t h a s b e e n d i s c u s s e d e l s e w h e r e in s o m e d e t a i l [2, 3].

2. P A R A G E N E T I C R E L A T I O N S IN S I M P L I F I E D S Y S T E M S AND T H E I R A P P L I C A T I O N TO NATURAL ASSEMBLAGES

2.1. Grosspydile and corundum eclogite F i r s t , a n i n t e r p r e t a t i o n of S o b o l e v ' s r u l e w i l l be presented. Let us examine the paragenetic relationships in the system A1203-CaSiO 3MgSiO3-NaA1Si206 under sufficiently high pressures, at which grosspydite (kyanite-free) and corundum eclogite assemblages are stable as s h o w n s c h e m a t i c a l l y in fig. 2 *. It i s not n e c e s * This paragenetie relation was not i n f e r r e d f r o m the study of simple s y s t e m s , but from an analogy with natural paragenetic relations, especially of inclusions in k i m b e r l i t e . It is possible that the clinopyr o x e n e - c o r u n d u m assemblage has no stability field in any combinations of p r e s s u r e and t e m p e r a t u r e , unless the s y s t e m contains other components such as f e r r o s i l i t e and jadeite. To deal with an explicit e x p r e s s i o n of the equilibrium relations, however, we need equations to i n t e r r e l a t e the thermodynamic p r o p e r t i e s of various phases, and the equilibrium relation in fig. 2 is presented to help the u n d e r s t a n d ing of these equations to be d i s c u s s e d later. If, for example, t h e r e is no real solution for eqs. (6) and (7), when we put Z = 0, it means that continuous g r o s s u l a r - p y r o p e solid solution is stable instead of a j a d e i t e - f r e e clinopyroxene-corundum a s s e m b l a g e . The validity of eqs. (6) and (7), however, is not affected by this.

sary that there should be a real physical envir o n m e n t in w h i c h s u c h a p a r a g e n e t i c r e l a t i o n s h i p is realized for the simple A1203-CaSiO3-MgSiO3 system. Throughout the following discussion, grossular-pyrope s o l i d s o l u t i o n i s a s s u m e d to b e i d e a l , b u t not n e c e s s a r i l y c o n t i n u o u s in a g i v e n p h y s i c a l e n v i r o n m e n t . A s to p y r o x e n e , l e t u s first consider the simplest model in which diopside forms an ideal solid solution with jadeite, f o r m i n g o m p h a c i t e , w h i c h d o e s not d i s s o l v e C a Tschermak's and clino-enstatite components. In t h e f o l l o w i n g , d i o p s i d e , c o r u n d u m , g r o s s u l a r a n d p y r o p e a r e d e n o t e d b y D, C, G a n d P a n d t h e r a t i o C a / ( C a + Mg) of g a r n e t b y X. C h e m i c a l p o t e n t i a l s a r e d e n o t e d b y t~ a n d tto, t h e l a t t e r r e p r e s e n t s t h e c h e m i c a l p o t e n t i a l of a p u r e component (molar free energy), and activity is d e n o t e d b y a. F o r c o n d i t i o n s of e q u i l i b r i u m b e t w e e n c o r u n d u m , g a r n e t a n d o m p h a c i t e , we h a v e t h e f o l l o w ing relationships: 3 CaMgSi206 + 2 A1203 = Ca3A12Si3012 + Diopside

Corundum

Grossular (1) + Mg3A12Si3012

•

Pyrope 3~D + 2~C = ~G + ~P • Since members

(2)

diopside, grossular and pyrope are of s o l i d s o l u t i o n s , eq. (I) m a y b e r e -

EFFECT

OF JADEITE COMPONENT

tionship between X and Z is obtained by the following s i m u l t a n e o u s equations:

written 3(~)+RTlnaD)

+ 2~

= (~+

251

3RTlnX)

X(1 - X ) + (~+

f r o m which the following r e l a t i o n s h i p is d e r i v e d be tw e en the g r o s s u l a r content of garnet, X, and the a c t i v i t y of diopside in c l i n o p y r o x e n e solid solution, aD: o + 2p~)R T l n X ( 1 - X ) = {(3PD + RTlna

(p~+ .~)}/3

D = AG 1 + R T l n a D .

(3)

Thus if we know the equation between the a c tivity and the mole f r a c t i o n in c l i n o p y r o x e n e , we can obtain the r e l a t i o n s h i p between the g r o s s u l a r content of g a r n e t and the j a d e i te content of o m phacite. Now let us take two s i m p l e m o d e l s for the r e lationship between a D and the m o l e f r a c t i o n of diopside in omphacite, which is denoted by Y. They a r e a D = Y,

(4)

X2(1 - X ) = K 2 a D a C T

,

(9)

X(1 - X) 2 = K 3 a E a C T

,

(10)

in which a E and a C T r e f e r to the a c t i v i t i e s of c l i n o e n s t a t i t e and of C a - T s c h e r m a k ' s c o m p o nent, r e s p e c t i v e l y . The f i r s t equation is obtained f r o m eq. (3), by substituting K 1 = exp ( A G 1 / R T ) . The second and t h i r d equations c o r r e s p o n d to the following c h e m i c a l r e l a t i o n s : 3 CaMgSi206 +

The f i r s t r e l a t i o n s h i p , eq. (4), c o r r e s p o n d s to a m o d e l in which t h e r e is r a n d o m m i x i n g of Ca and Na in the M I s i t e s , but the p o s i t i o n s of Mg and A1 in MII s i t e s a r e uniquely dependent on the p a r t i c u l a r co n fi g u r a t io n adopted in the M I s i t e s , i.e., it is a s s u m e d that the c o n f i g u r a t i o n of C a - M g and Na-A1 a r e coupled. The second r e lationship, eq. (5), c o r r e s p o n d s to the m o d e l in which C a - N a d i s t r i b u t i o n in M I and the Mg-A1 d i s t r i b u t i o n s in MII a r e both r a n d o m and i n d e pendent of each other. F r o m eqs. (3) and (4) and f r o m eqs. (3) and (5), we obtain the following r e l a ti ons h i p s between the m o l e f r a c t i o n of ja d e it e in o m p h a c i t e Z = N a / ( N a + C a ) and g r o s s u l a r content of g a r n e t X = C a / ( C a + Mg):

= 2 Ca3A12Si3012 + Mg3A12Si3012, (11) Grossular 3 Mg2Si206

+

(fora D= Y= l-Z)

(6)

Pyrope

3 CaA12SiO 6

=

Ca-Tschermak' s component

= Ca3A12Si3012 + 2 Mg3A12Si3012. (12) Grossular

Pyrope

T h e s e s i m u l t a n e o u s equations cannot be solved u n l e s s we know the r e l a t i o n between a c t i v i t y and m o l e f r a c t i o n in c l i n o p y r o x e n e solid solution. If we a s s u m e , however, that a c t i v i t y is equal to m o l e f r act i o n , we have the following equation b etween X = C a / ( C a + M g ) in g a r n e t and Z, the m o l e f r a c t i o n of jadeite in o m p h a c i t e : Z = AX 2 + BX + C ,

(13)

in which 1 - K2/K 3

AZ= 1 - X(1-X) K1

=

Ca-Tschermak's component

Clinoenstatite

2 .

3 CaA12SiO 6

Diopside

or

aD=Y

(8)

= Kla D ,

3 R T I n (1 - Z ) )

K 1

,

B : (2K2/K1K3) - 1/K 1 - K1/K 2 ,

Z = 1

_ (X(1 - X)~ ½ \ ~ ]

(for a D = y2 = ( 1 - Z ) 2 ) ,

(7)

in which K 1 = exp ( A G 1 / R T ) . E i t h e r of the c u r v e s obtained f r o m eqs. (6) and (7) by plotting X a g a i n s t Z, is s y m m e t r i c a l with a s y m m e t r y a x i s X = 0.5, at which Z is a m i n i m u m , and Z i n c r e a s e s as X d e v i a t e s f r o m 0.5. Next, let us take a g e n e r a l m o d e l w h e r e o m p h a c i t e c o n s i s t s of diopside, c l i n o e n s t a t i t e , C a T s c h e r m a k ' s and j a d e i t e components. The r e l a -

C : 1 - K2/K1K 3 .

F r o m eqs. (9) and (10), we obtain _Xx=

aD

F o r n a t u r a l and synthetic o r t h o p y r o x e n e - c l i n o p y r o x e n e - g a r n e t a s s e m b l a g e s X = 0.13 + 0.01 [4, 5]. The mole f r a c t i o n of diopside is g r e a t e r than that of c l i n o e n s t a t i t e in c l i n o p y r o x e n e in

252

S. BANNO

q u e s t i o n , t h u s we c a n a s s u m e a D >aE, s o t h a t w e h a v e K 2 / K 3 < 1. T h e r e f o r e , A > 0. T h e X - Z c u r v e t h u s o b t a i n e d i s a p a r a b o l a . If a E = 0, i . e . , o m p h a c i t e d o e s n o t c o n t a i n c l i n o e n statite component, then the parabola has the axis of s y m m e t r y a t X = ~ + ' /~1/2K2 ( K 2 / 2 K 1 > 0). In natural grosspydites and eclogites, the orthopyr o x e n e c o n t e n t of c l i n o p y r o x e n e i s u s u a l l y low, so the X - Z curve may be a parabola with a symm e t r y a x i s a t X > 0.5. The data from natural grosspydites and eclog i t e s d e s c r i b e d b y S o b o l e v et al. [1] s h o u l d , therefore, be connected by a curve, with a minim u m a t X > 0.5. T h e b r o k e n l i n e in fig. 1 g i v e s t h e a u t h o r ' s i n t e r p r e t a t i o n of t h e o b s e r v e d d a t a . F r o m t h e d i s c u s s i o n s g i v e n a b o v e , it i s c o n c l u d e d t h a t t h e r e i s a s o u n d b a s i s to S o b o l e v ' s r u l e a n d t h e r e l a t i o n b e t w e e n N a 2 0 of o m p h a c i t e a n d t h e C a / ( C a + Mg) r a t i o of a s s o c i a t e d g a r n e t i s not f o r t u i t o u s . S i m i l a r t r e a t m e n t c a n b e a p p l i e d to t h e a n a l y s i s of o t h e r e c l o g i t e a s s e m blages. 2.2. Kyanite eclogile The relationship between the jadeite content of o m p h a c i t e a n d g r o s s u l a r c o n t e n t of g a r n e t in k y a n i t e - q u a r t z e c l o g i t e c a n b e d e r i v e d in t h e same way as discussed above. The mathematical e x p r e s s i o n of c o r u n d u m - b e a r i n g and kyanitequartz-bearing equilibria are the same except for the constants involved. In k y a n i t e e c l o g i t e s d e s c r i b e d in t h e l i t e r a ture, the clinopyroxenes are all omphacite with a n a p p r e c i a b l e a m o u n t of t h e j a d e i t e c o m p o n e n t . T h u s t h e g r o s s u l a r c o n t e n t of t h e c o e x i s t i n g g a r n e t s i s , in a l l c a s e s , l e s s t h a n t h e m a x i m u m a t tainable under the same physical conditions in the simple jadeite-free system.

of C a - T s c h e r m a k ' s component in omphacite associated with garnet and orthopyroxene is small, s o t h a t a D i s m a i n l y d e t e r m i n e d b y t h e a m o u n t of t h e j a d e i t e c o m p o n e n t in o m p h a c i t e . A s s u m i n g t h a t a c t i v i t y i s t h e s a m e a s m o l e f r a c t i o n , we o b t a i n t h e f o l l o w i n g r e l a t i o n b e t w e e n X a n d Z: Z : (1 - a E ) - (K3aE//K2)(X/1 - X) - (1/g3aE)Z(1

-)0 2 ,

(15)

in which a E is a constant, dZ/dX< 0 when 0 < X < ~ f o r a n y v a l u e s of t h e c o n s t a n t s i n v o l v e d . F r o m p e t r o g r a p h i c a l a n d e x p e r i m e n t a l d a t a , we k n o w X = 0.12 - 0.14 w h e n Z = 0 [ 4 , 5 ] , t h u s 0 ~< X --< 0.14. It i s c o n c l u d e d t h a t t h e g r o s s u l a r c o n t e n t of g a r n e t d e c r e a s e s a s t h e j a d e i t e c o n t e n t of a s s o c i a t e d o m p h a c i t e i n c r e a s e s . In o r d i n a r y e c l o g i t e , w h i c h d o e s not c o n t a i n either corundum (or kyanite-quartz) or orthopyr o x e n e , t h e X - Z r e l a t i o n s h i p i s not u n i q u e e v e n in a FeO-free system, as bimineralic eclogite h a s o n e m o r e d e g r e e of f r e e d o m t h a n h y p e r s t h e n e e c l o g i t e . If, h o w e v e r , t h e r a t i o A1 : C a : Mg of t h e s y s t e m i s g i v e n , we h a v e a g a i n a u n i q u e r e l a t i o n b e t w e e n X a n d Z, a n d t h e C a c o n t e n t of g a r n e t d e c r e a s e s a s t h e j a d e i t e c o n t e n t of o m p h a c i t e i n c r e a s e s . It i s t h u s p o s s i b l e t h a t t h e g a r n e t s of s o m e b i m i n e r a l i c e c l o g i t e s a r e l e s s calcic than the garnets associated with clinoand orthopyroxenes in a Na20-free system.

3. E X A M P L E S IN N A T U R A L ROCKS In n a t u r a l

clinopyroxene-orthopyroxene-gar-

2.3. Hypersthene eclogite General relation. T h e e f f e c t of t h e j a d e i t e c o m p o n e n t on t h e c o m p o s i t i o n of g a r n e t i n h y persthene eclogite can be obtained in the same manner as above. F r o m e q s . (9) a n d (10), we o b t a i n e d t h e f o l lowing equation X/(1-X)

: (K2/K3)(aD//aE) .

CaO Wt~ GARNET

(14)

B e c a u s e t h e c o m p o s i t i o n a l r a n g e of e n s t a t i t e in e n s t a t i t e e c l o g i t e i s s m a l l , l e t u s a s s u m e t h a t enstatite has the stoichiometric composition MgSiO 3. T h e n t h e a c t i v i t y of t h e c l i n o e n s t a t i t e c o m p o n e n t in c l i n o p y r o x e n e i s c o n s t a n t , s o t h a t under a given temperature and pressure, X is a f u n c t i o n of t h e a c t i v i t y of t h e d i o p s i d e c o m p o n e n t in c l i n o p y r o x e n e . In n a t u r a l r o c k s , t h e a m o u n t

4

I 2 Na20 WI~

I 3

CPX

Fig. 3. The relation between CaO wL % of garnet and

Na20 wt. % of omphacite from hypersthene eelogite inclusions f r o m Salt Lake, Hawaii. Data a r e from Yoder and Tilley [6] and White [7].

E F F E C T OF JADEITE COMPONENT Ca 50**

253

Ca 50%

Ol

o3

Mg

Fe

Fig. 4. The Ca:Mg:Fe r a t i o s of garnet f r o m inclusions in k i m b e r l i t e . Solid circle: garnet from garnet lherzolite inclusions in k i m b e r l i t e from OVHara and Mercy [4], Nixon, K n o r r i n g and Rooke [10], Sobolev [11]; open circle: g a r nets of eclogite. Numbers c o r r e s p o n d to those of table 1. n e t e q u i l i b r i u m , w e m u s t t a k e t h e e f f e c t of M g Fe substitution into consideration. If, h o w e v e r , w e a r e d e a l i n g w i t h r o c k s w i t h s i m i l a r F e 2 + / M g r a t i o s , t h e e f f e c t of M g - F e s u b s t i t u t i o n m a y b e i g n o r e d . Fig. 3 s h o w s t h e r e l a t i o n b e t w e e n C a O wt. % of g a r n e t a n d N a 2 0 wt. % of o m p h a c i t e f r o m h y p e r s t h e n e e c l o g i t e s f r o m Salt Lake, Hawaii, as described by Yoder and T i l l e y [6] a n d W h i t e [7]. I n s p e c t i o n of t h e f i g u r e reveals that the X-Z relation discussed above is in agreement with the trend in natural rocks. In fig. 4, s o l i d c i r c l e s r e p r e s e n t t h e C a : M g : F e r a t i o s of g a r n e t s f r o m g a r n e t p e r i d o t i t e i n clusions in kimberlite, which are associated

w i t h N a 2 0 - p o o r (< 2 wt. % N a 2 0 ) c l i n o p y r o x e n e a n d o r t h o p y r o x e n e . A c c o r d i n g to t h e p r e v i o u s discussion, garnet associated with Na20-poor clinopyroxene, but without accompanying orthop y r o x e n e , s h o u l d f a l l a b o v e t h e a r e a of t h e s o l i d c i r c l e s in t h e f i g u r e , a n d m o s t of t h e g a r n e t s f r o m e c l o g i t e i n c l u s i o n s in k i m b e r l i t e o r k i m b e r l i t i c d i a t r e m e s do f a l l a b o v e t h i s . H o w e v e r , t h e r e a r e a few e c l o g i t i c r o c k s w h o s e g a r n e t s f a l l b e l o w t h e a r e a . T h e a n a l y s e s of g a r n e t a n d o m p h a c i t e f r o m s u c h r o c k s a r e l i s t e d in t a b l e 1. T h e r a t i o s of C a - T s c h e r m a k ' s , wollastonite a n d o r t h o p y r o x e n e c o m p o n e n t s of t h e s e o m p h a c i t e s a r e l i s t e d i n t a b l e 2. It i s w o r t h n o t i n g t h a t

Table 1 Chemical compositions of omphacite and garnet from eclogitic rocks with unusually low CaO garnet. CPX *

GAR *

CPX **

GAR **

SiO 2 TiO 2 A1203 Fe203 FeO MnO MgO CaO Na20 K20 H2 O+ H20Cr203 NiO

55.3 0.51 6.0 1.71 4.57 0.13 11.7 14.7 4.08 0.18 0.7 0.0 0.15

41.27 0.46 22.03 0.83 14.94 0.45 16.11 3.89 0.13 0.09 0.07 0.10 0.20

52.69 O.73 6.93 1.20 1.22 0.023 16.05 17.10 2.80 0.06 0.82

44.12 0.35 22.72 2.85 5.34 0.26 20.63 4.04 0.03 0.05

0.30

0.26

Total

99.73

100.57

99.92

100.65

CPX ~-

GAR ~"

56.39 0.22 13.74 4.66 1.24 0.11 6.70 7.73 9.01 0.06

39.31 0.35 22.03 1.07 24.00 0.74 9.52 3.35 0.08 0.03

0.01 0.0022 99.87

0.001 0.002 100.48

* Eclogite inclusions in k i m b e r l i t e , f r o m R o b e r t s - V i c t o r mine, South Africa. Analyst: H. H a r a m u r a . Optical p r o p e r t i e s CPX: (~ = 1.680, fl = 1.686, T = 1.701 (0 =~ 0.002), garnet: n = 1.757 =L0.003. The sample is housed in the Geological Institute, University of Tokyo. ** Eclogite inclusion in k i m b e r l i t e from Obnadgennaya pipe, Yakutia, Sobolev and Kuznetsova [12]. ~ ~Eclogite n (clinopyroxenite with a little garnet and ruffle) f r o m Arizona d i a t r e m e (GK-6), O'Hara and Mercy [8].

254

S. BANNO

Table 2 The ratios Ca-Tschermakts, wollastonite and orthopyroxene components of clinopyroxene, and ratios Ca : Mg : Fe of associated garnets from eclogitic works in table 1.

CaAI2SiO 6 Ca2Si206 (Mg, Fe)2Si206 GAR Ca Mg Fe

1

2

3

0.01 0.42 0.57

0.08 0.37 0.55

0.11 0.35 0.54

0.103 0.59 0.31

0.109 0.78 0.11

0.095 0.38 0.53

t h e y a r e r i c h in C a - f r e e p y r o x e n e c o m p o n e n t and p o o r in C a - T s c h e r m a k ' s c o m p o n e n t . In the N a 2 0 - f r e e s y s t e m , r o c k s with c o m p o s i t i o n s lying on the Mg(+ F e 2+) side of the g a r n e t - c l i n o p y r o x e n e f i e l d (fig. 2) w o u l d c o n t a i n c l i n o p y r o x e n e s low in C a - T s c h e r m a k ' s component and r e l a t i v e l y high in M g S i O 3 ( + F e S i O 3 ) , and g a r n e t w i t h g r o s s u l a r c o n t e n t s only s l i g h t l y g r e a t e r than t h o s e of the h y p e r s t h e n e e c l o g i t e a s s e m b l a g e . In the p r e s e n c e of m o d e r a t e o r l a r g e a m o u n t s of j a d e i t e in the c l i n o p y r o x e n e (as in the s a m p l e s of t a b l e 1), the g r o s s u l a r c o n t e n t of the g a r n e t of t h e s e a s s e m b l a g e s w o u l d be f u r t h e r r e d u c e d g i v i n g tie l i n e s a p p a r e n t l y c u t t i n g the g a r n e t - c l i n o p y r o x e n e - o r t h o p y r o x e n e f i e l d of the A C F d i a g r a m . T h e high j a d e i t e c o n t e n t of t h e s e o m p h a c i t e s c a u s e s f u r t h e r r e d u c t i o n of the g r o s s u l a r c o n t e n t of a s s o c i a t e d g a r n e t s , so that the g a r n e t s of t h e s e p a r t i c u l a r e c l o g i t i c r o c k s a r e p o o r e r in g r o s s u l a r than t h o s e f o r the two pyroxene-garnet eclogitic assemblages. This s u g g e s t s that the low CaO c o n t e n t of t h e s e g a r n e t s c a n be e x p l a i n e d in t e r m s of the e f f e c t s of j a d e i t e a s d i s c u s s e d a b o v e , and n e e d not n e c e s s a r i l y be a s c r i b e d to u n u s u a l p h y s i c a l c o n d i t i o n s of f o r m a t i o n . It is p o s s i b l e that the e c l o g i t i c r o c k f r o m A r i z o n a , USA, d e s c r i b e d by O ' H a r a and M e r c y [8], w a s f o r m e d u n d e r d i f f e r e n t p h y s i c a l c o n d i t i o n s f r o m o r d i n a r y i n c l u s i o n s in k i m b e r l i t e , a s s u g g e s t e d by t h e m s e l v e s . It is not b e c a u s e of the low g r o s s u l a r c o n t e n t of the g a r n e t , but b e c a u s e of the f a c t that the p a r t i t i o n of Mg and F e 2+ b e t w e e n g a r n e t and o m p h a c i t e is quite u n u s u a l , w i t h an a p p a r e n t p a r t i t i o n c o e f f i c i e n t c o m p a r a b l e to the v a l u e s of l o w - t e m p e r a t u r e e c l o g i t e in g l a u c o p h a n i t i c m e t a m o r p h i c t e r r a n e s [9]. 4. S U M M A R Y AND C O N C L U S I O N On the b a s i s of the a n a l y s i s of the p a r a g e n e t i c r e l a t i o n in a s i m p l e h y p o t h e t i c a l s y s t e m , a g e n -

e r a l r e l a t i o n s h i p b e t w e e n the j a d e i t e c o n t e n t of o m p h a c i t e and the g r o s s u l a r c o n t e n t of a s s o c i a t e d g a r n e t in e c l o g i t i c r o c k s h a s b e e n d i s c u s s e d . M a t h e m a t i c a l e x p r e s s i o n s of t h i s r e l a tionship are presented for some simple models on the a c t i v i t y - m o l e f r a c t i o n r e l a t i o n s h i p in c l i nopyroxene solid solution. In c o r u n d u m e c l o g i t e , k y a n i t e - q u a r t z e c l o g i t e and h y p e r s t h e n e e c l o g i t e , the g r o s s u l a r c o n t e n t of g a r n e t d e c r e a s e s w i t h i n c r e a s i n g c o n t e n t of a l k a l i in the p y r o x e n e s . In g r o s s p y d i t e , the g r o s s u l a r c o n t e n t of g a r n e t i n c r e a s e s w i t h i n c r e a s i n g a l k a l i p y r o x e n e c o n t e n t s of o m p h a c i t e . S o b o l e v ' s r u l e found d u r i n g the study of g r o s s p y d i t e and a s s o c i a t e d e c l o g i t e x e n o l i t h s can be e x p l a i n e d by t h i s , a s w e l l a s the r e l a t i o n b e t w e e n the CaO c o n t e n t of g a r n e t and the N a 2 0 c o n t e n t of o m p h a c i t e in H a w a i i a n h y p e r s t h e n e eclogites. It is a l s o s u g g e s t e d that the f a c t that s o m e e c l o g i t i c i n c l u s i o n s in k i m b e r l i t e c o n t a i n low C a O - g a r n e t d o e s not n e c e s s a r i l y i m p l y u n u s u a l p h y s i c a l c o n d i t i o n s of t h e i r f o r m a t i o n . ACKNOWLEDGEMENTS T h i s w o r k w a s done w h i l e the a u t h o r w a s a v i s i t i n g f e l l o w in the D e p a r t m e n t of G e o p h y s i c s and G e o c h e m i s t r y , A u s t r a l i a n N a t i o n a l U n i v e r s i ty. He is d e e p l y i n d e b t e d to P r o f e s s o r A. E. R i n g wood, Dr. D. H. G r e e n and Dr. A. J. R. W h i t e f o r d i s c u s s i o n on the s u b j e c t and the c r i t i c a l r e a d i n g of the m a n u s c r i p t ; a l s o to Mr. H. H a r a m u r a of the U n i v e r s i t y of T o k y o f o r the c h e m i c a l a n a l y s e s of m i n e r a l s . T h e a u t h o r a s s u m e s s o l e r e s p o n s i b i l i t y f o r the c o n c l u s i o n s . REFERENCES [1] N.V.Sobolev, N.I. Zyusin and I.K.Kuznetsova, Dokl. Akad. Nauk SSSR 167 (1966) 902. [2] S. Banno, Japan. J. Geol. Geogr. 35 (1964) 115. [3] S. Banno, N. Jb. Min., in p r e s s (1967). [4] M. J. OVI~ara and E. L. P. Mercy, Trans. Roy. Soc. Edinburgh 65 (1963) 251. [5] M.J.O~Hara, Year Book 62, Geoph. Lab. (1963) 116. [6] H. S. Yoder and C. E. Tilley, J. Petr. 3 (1962) 342. [7] R. W. White, Contr. Min. Petr. 12 (1966) 245. [8] M.J. OVHara and E . L . P . Mercy, Amer. Min. 51 (1966) 336. [9] S. Banno and Y. Matsui, Proc. Japan Acad. 41 (1965) 716. [10] P.H.Nixon, O. Von Knorring and J.M.Rooke, Amer. Min. 48 (1963) 1090. [11] N.V.Sobolev, Paragenetic types of garnet (Moscow, 1964}. [12] N.V. Sobolev and I.K. Kuznetsova, Dokl. Akad. Nauk SSSR 163 (1965) 471.