American ournal of Science
A REDETERMINATION OF EQUILIBRIIJM RELATIONS
BETWEEN ZSYANLTE AND SICLIMANITE
SYDNEY P. CLARK, JTL
Geophysical l;al~oratory, Carnr:gic Institution
Washillgtox~,D. C.
o f Wnsl~ington,
A.BSTRACT. Thc equilibri~lrncurve I.mt~vecnkymile and sillimarzite has 1.1eencstnblisl~ecl
by q u e n c h i n g cxpwirncmls at ~x:mpernturc.s bc?l;wesn 1000°C and 1500°C and pressures between 17 a n d 24 kiloburs. Tltr: curvc. is given by tlie expressian P = 4.1 1- 13.2 X lO-' I',
whare tho pressure, P, is i n kilolmrs n11c-l the temperutucc, T, is in degrees Centigrade.
There i s some evidcnce that the ~ h n s aboundary mny dcpnrt from Iinenri~yat low temperatures, but; 110 quantitative ctstirnntc: o:f ~ l l crlmounl: 0.f curvature can lac o h i n e d from
present data.
If kynnite forms s ~ a b l yin nature, prcs,surcs of nearly 10 kilol.~arsare required, This is
ccpxivalenl: t.o the wcigl11:of nl.)oul: 30 kilornc:ec?rs nE ovt:rlmrtlen. S11c11 great depths of burial
are n o t requ.ircc1 if pressure is c:ontninc?d 11y 1:11cst.~:engehns ~ v d las by the weight of the
overlying rock. 11; is s u g g e s t d t h l : "twtonic ovt?rprossures" ol: n kilobm or mom may
exist in socks which a r e undergoing d c h m m t i o ~ n .
T h e inversion oS kynnitc to sillimnnite is the simplest of: tlkc elslssicnl
metamorphic isograds
to characterize chemi.cally. 130th mi.neuals are close ,to
A12Si0.5 in composition, with otlwr elerncn~susually prcscmt in very small
amounts. 1-1cn,ce,they may he regarded as jmrc phases of tlir: same composition,
a n d -their equili1.1rium relations arc-: tlierefore unil8ccted Ijy complicating factors
such as the-lmlk composition of the rock in which they occur-or pnr~ialpresThe de.termi.nation of their fields of stability in
sures of volatile components.
the laboratory carries direct jmplications
nlmut the conditions uncles which
they were formcd in rocks, subjcct: only to he assumption that chcmical equil i h r i u m is closely
i n nature.
- apprnacliecl
-T h e cliemical simplicity of ,these phases does n0.t imply ,i:Xlitt reactions involving them arc easy to produce in the lahoratnry. Botlz are extremely refractory and react with great reluctancr: at temperatures below 1000°C. In earlier
work on ,thi,s system (Clark, Rolnertson, and Birch, 1957), the .temperatures
r e q u i r e d for reaction to takc placc in a reasonaldc time were uncomfortably
close to the maximum attainable. Thc nurnher 01 strccessf~druns at high temperatures was limited b y failure of the apparatus, and the revcrsildity of the
reaction was perhaps not cZemonstratecI as convincingly as one might clesire. A
phase boundary, basecl largely hut not entirely on syntheses of kyanite or sillirnanite, was es'tnblislzed between 1000°C and 1300°C, despite these clificultics.
It is comparatively easy to maintain high temperahires and pressures for
extended periods of time in apparatus in which pressure is transmitted by a
plastic solid and the charge is bea,ted by a tuhular graphite heating element.
Such apparatus has the disadvantage that the pressure must be calculated from
t h e force applied to the piston which procluces it, and correci5ons for friction
and the finite strength of the pressure-transmitting medium must he made. In
The present work was done in a.pparatus that diflcrs only i n minor rcspects from that described by Boyd a i d England (1960). Calihmtion against
the 13i I-Bi I1 transition, which takes place n t 25.2 kiIolmrs nr; 2S0,C, indicates
,that the pressurc calculated from the lond on t l ~ :piston is greater than .thnt
experienced by the sample by about 13 pcxcent at room .tmpcraturo. This
figure is reprodu~cibleto within a fcw tenths o:f one pr\rcc:nt. P a r t of this lass of
pressure is attributable to the strength of ,the talc slctcvc? whkh transmits the
pressure. This will be lower at high temperatures, implying that a correction
gi.vnn l>c?lowhavc bcen
of less than 13 percent should be made. Thc ~~rc?ssnrc!s
determined by reducing the value cnlculatwl l r o m tho lond on the piston by
8 percent of the corrected pressure, in agrccmtxt wid1 thc prncti,ce o f Boyd
and England. The pressure calculated in this way is l~cli.c!vr?d
.to h e accurate to
within 5 percent for the range of pressures ihrough which the rcnction could
I x followed in the present study.
Temperatures of the charges were rncasrzretl wid1 Pt-Pt LO pcrccnt Rh
~tliermocouplespressed against one encl of the PI:c:npsule in which thc ~hnrgc?
was lield. The thermal gradient in ,tlic Purrzacc r a r d y cxcccc2ecl 15OC in the
length of the charge and never exceedccl ZO°C. No corrc!c:ticln was anade for tlii:
effect of pressure on the e.m.f. otf -the thcrmot:ouple.
Four materials were used as rc?nctnn.ts in .this study. ICyani-te and s411imanite were synthesized from an,clalusite Prom Hill City, South Dakota and
Irom rnrtakaolinite prepared by firing Georgi,a knolinitc: overnigl.lt. a.t GOO°C.
The kaolinite, kindly supplied by G. C. Kennctly, contained as principnl impurities 0.15 percent Na,O and 0.30 percent TiO, (analysis by C. G. Engcl).
No analysis of the ancldusite i s available. Kyani.tr: ;horn J3uunsvi.lle, N o r h
Carolina and sillimanite :from Brandywine Springs, Dclnware werc also used
in -the experiments. An analysis o;E the kyanite Inns lxcn given by Todd (1950)
The sillimanite is probably very pure, judtging by its lack of color and -the rdn,tivcly small values of its lattice parameters (Skinner, Applemnn, and Clark,
1961) . Fine-grained samples of the aluminosilicarcs werc: prepared b y clatriat.ing in water for 6 minutes.
Experimental results are givcn i n table 1 and a r c shown in figurcs 1 and
2. Products were identified by their X-ray cliDraction palterns. The phase
boundary in figure 2 is the same as that dctcrmincd by the syntheses shown in
figure I. This boundary is reversible to within a kilolar, and he rcsults of the
experiments are insensitive to the particular rsclclant used, This conclusion was
+
Equilibrium Relations bctwecn Kyarzite tartd Sillimnnicc
643
TABLE1
Expcrimcxltnl Results
"C
Temperature
Kilnbnrs
Pressure
I-Iours
D r r r a ~ i a ~ i 1tcnckan1.s
Products
MK, melakaolinite; A, nndalusite; K, kymite; S, sillirnnnite; G, glass; Q, quartz; C,
ao rtmdum.
Pnrentheses indicate phase present in minor amounts.
"Metastable phase.
arrived at previously (Clark, Robertson, and Birch, 1957), but the present
evidence is much less equivocal.
Kyanite and siilimanite were synthesized together in several runs close to
thc equilibrium curve. This is probably due to small gradients of pressure and
temperature. The persistence 01 both phases can be attributed, in part at least,
to the extreme sluggishness with whi#ch reaction between kyanite and sillimanite takes place close to the equilibrium curve.
Attempts were made to locate the equilibrium curve at temperatures below 1000°C, using as a reactant metakaolinite seeded with about 10 percent
each of kyanite and sillirnanite. In runs 1 kilobnr or more away from the extrapolated phase bousdary at 900°C, the polymorph stable under the conditions of the experirn&t was docidedly the more plentilul product of the run.
The results of runs closdr to the equilibrium curve were not sufficiently clearcut
Pressure, kilobars
to permit hem to be assigned d e f i n i ~ c to
l ~ c i ~ h r rfirlcl of s t u l ~ i l i ~R
y .o ~ hkynnitc
and sillimanite grew i n about equal amozzuts.
Several experimenls in which thc rchnctan I; was cith or kntslini~eor an
prcssurcs. The water content of ~ l i c wc:hczrgw is 3 2 0 ~ rc~nllyknown, nr; it was
not possible to demonstrate the alosclncc: o f lcnk (luring L-IW run. Thcsct okservat i m s of melting are of only cjualitativt. vnluc as a sc~sult.The nppmmnce 0.E
corundum in these experimcnts i s of intcrt?st: Iwcausc i ~ s: u g g c s ~ sa passiblc
explanation of the metastable formation o I quartz plus corundum ihut pIug11ctI
the previous study (Clark, Robertson, and JE3irc:lr, 1957). T i 1 dmse suns, kaolinile or andalusite which contained pyropliyllito as a n irnpurit y wcrr: h a l e d in
unsealed capsules. It is passihlc that partial Eusion and lllc ntdleatinn of
corundum took place before a11 h e water ivc-aped OHCCCormctl, corun durn will
persist practically indefinitely. The appcauancc: of this mctasta1)lc ussernhlngr:
was not troublesome in the present work.
COMPARISONS WITH OTT-IEIZ W O R K
The present results are compared w i h those of the provious study (Clark,
Robertson, and Birch, 1957) in Ggure 3. Wilhin ~ h common
c
rangc. of experiment (lOOO°C to 1300°C) the two sets o l data agrcc to within 1 kilohar. The
discrepancy could be reduced by applying a smaller correction l o r friction and
the strength of the pressure medium to the prrscmt rrsults, but the cliflercnce is
probably within experimental error as it stands. It may also br n measure 01
the width of the zone of indiflerence between kyanitc and sillimahite.
Pressure, kilo bars
Fig. 2. Condi~ionsunrlt!r wliich LIK? rawlion was revcrsr:d. Solid squares represent
sillim,zni~c:formt:tl Irorri kyuni to, solid circles rcr?prcscnt k y m i l e folmcd from sillimanite,
n n d open squares rcbprcsc?n~
uncifT(:clutl kyuai~e.
r 7
I he ccurvcts :in figure 3 have.?
l w r m sai~~apolt~~:r!tl
t o low temperatures without
r e g a r d Ssr othctr rtxzctjclus tlmt compli.cutc: thu stuble pl~asediagram. Natural
cxc;urrenc:c?s suggest: t l ~ csistcnc:c!
:
of a ~riplc::1 ) o i 1.wtwcen
~
anclalusite, kyanite,
nncl. s i l i m a n i t e a't moilcl*iztc tr?mpcrat~ircsanci prcssuxs, 21: has also been suggc?stc.d, aIt1~oughnot clc?mo~.~strntc:tl,
that ( x ~ i t r pl~wcorunclurn
t~
lmve a field of
s-takdity (Aramaki und Roy, 1958). This suggctstion clocs not agree well with
mtura.1 cvidmc;e; in .the rart: ,cases in w l k h .~llc:y110th occur in the same rock,
p a ~ ne
uC1~cmruntlurn a r c usually st.pratecl from each other by an alurninous
silicate. One of the connnoncst occmxmces o f mnrgarite is as a coating surro~lndingcorundum crystals in quurtzosc rocks (Pmti: and. Lewis, 1905).
The s l o p ol the phusc: J.,nilndnsy determinod in the present study is 13.2
l.mrs/degrce. This is sligldly larger than ~ l vnlrrc
~ e found previousIy (about 10
hars/degrec), but it is decicleclly srnallcr than .the slope cnlculatecl from roorntemperature ~tlzermt>cl.lc;micu.~xmomil clnta. Tutld (1950) Eouncl that -the: change in ent r o p y crf ,the reac~ionat room ternl~ei-atirrcwas 1 2 3 5 ~ 6clecijoules/mol°C, and
a n extensivr study of thc lattice pururnctars of kynnite and sillimanite (Skinner,
Clark, and Applcmun, 1961.) s'hows that thc chixagc in volume is 5.80c0.03
c:rn3/rnol. According t o theso fi,goros, the s l o p ol the phase boundary is 21.22
1.1 bars/degrec:.
High-tcrnpcrature X-ray studies at n tmasplieric pressure (Skinner, Clark,
and Appleman, 1961.) sliow that kyanitc has u larger thermal expansion than
sillimnnitc a t moderate tcrnperatores. ( ~ A V / ~ ) T )is~ about.
. = ~ 0.4 X lo-'
crn"/mole OC at 200° C and clecrcases at higher temperatures. The net decrease
in AV between O0 and 1000°C is about 3v2percent. It is unlikely that this
result will be greatly nltr:red a t the pressures of the equilibrium curve. The
en[ect of pressure on A V is likely to be no larger .than the eflect of temperature
Sydney P. Clark, Jr.-A
R s d c ~ e r r n i n u ~ iof
o~~
Depth , kilometers
Pressure, kilobars
Fig. 3.
Comparison with previous work. Curves A and B are ihe curves given by
Clark, Robertson, and Birch (1957, fig. 2).
according to the argument given previously (Clark, Robertson, and Birch,
1957).
The effect 01 pressure on AS, the entropy change o l the reaction, is given
by the Maxwell relation ( d ~ s / d P=
) ~- ( t l ~ T / / d T ) ~At. high temperatures
the pressure effect is small becanse ( a a Y / d T ) is small, and a t low temperatures it is small because the pressures of the equilibrium curve are low. The
increase i n A S is unlikely to exceed 3 percent under any conditions. The cflect
of allowing for the derivatives of volume and entropy discussed so far is to
increase the slope of the phase boundary, in conflict: with the experimental results. But the predicted increase is much less than the reduction i n slope of
about 50 percent that is required to secure agreement between the high-ternperature, high-pressure experimental results and the room-temperature thermochemical data.
Measurements of heat capacity at high temperatures (Kelley, 1949) indicate that a change in A S with temperature may alter the slope of the phase
boundary by roughly the amount required to bring the two sets of data into
agreement. The change in slope may be uncertain by as much a s 50 percent,
however, and no account was taken ol: the correction in drawing the phase
boundary i n figure 3 for this reason. Because heal. cnpaci~iesof solids usually
depart most widely from their classical values at low temperatures, most of the
curvature probably takes place below 500°C. Hence the position 01the phase
boundary will not be greatly affected by this correction.
r -
l l i c hi& pribssurcs rcyuirecl to lorm kyaiiitc stably, wliich wcre an unc x p c c ~ c drusuh 01 1110 previous work (Clark, RoLcrtson, and Biwh, 1957), are
Ly tlxc prcscM stucly. Tcmpr:raturcs of a Icw hundred degrees
subsi.nn~ia~ct3
secni to I>c required 10 prod~zcc:rcgriond metamorphism, which means that: a
l'ressurc ol: 7 LO 10 kilotars is roagldy tlic rnirlirn~rnlcompatible with stable
formation 06 kytini~oin mturc.
Depths of Lurid arc commonly r t h c i l to pressure by P = p gh, where
is t h c mcau dcnsity bctwcen the surface and du1pt.h h, and g is .the gravitational
occcleraiion. The scnlc at thr rt~pol: figure 3 has been calc~llatcdlor p equal
to 2.G7 grn/crn:' in tlic crust a i d 3.33 gm/cms in the m a d e . A depth of more
tllan 35 km is requirccl to reach a pressnre a1 10 kilobars; this implies that
p
kyanite scliists formed at c'lep~lisccpivalcnt to those towards the base of the
n o r r n ~ z l 'sea-lcvcl
~
crusl, 0x1 h i s moclcl. Tliis co~iclusiondoes not follow if the
phase boundary has apprcxiable curvature at high ternpcralures, but such behavior, altlzciugh nc.)t impossible, is ccrlainIy irnprobilblc.
Tf kyanitc-bcaring rocks are t o be Sormccl n.t depths in excess of 20 km,
l a r g e vertical rnovclncnts must have tnkan place in the past. Such large amplitu,dcs of motion might accompaxly thc formrrtiorl of a major mountain root,
Bu.t .they seem unlikdy to rcsult horn less extreme omgenic episodes. The depth
required for the stnblc .%ormiatiorrof kyarlite in a mountain rcmt may be greater
than t h rcq~lirecl
~
elsewhcro l)c!cause o f the high .temperatures that may exist
in a thickcizrd crust (Birch, 1950 ; Clark and Niblett, 1956). This cou1d.lead
LO .the formation of zones of kyanite-,bearing rocks near the margins of the root,
w i t h sillirnanite in ,the central, hot portion. This is the spatial dis-tribution of
the alurninosilic~ltcsfound in Ncw I-Inmpsliire, for example (Billings, 1956).
'I'hesc grcat clcq~ths01 burial can be escaped, or at least lessened, if pressures in t h e crust arc sustained by the strength as well as the weight of the
overlying rack. The mere existence o f deformation in metamorphic terrains
implies tlaut stress ilifierences exceeded the strength of the rocks, and the nature
o f -thc cleformation suggests that the stresses causing i t were compressive relativc .to p g h rather .than -t;ensi.le. This implies .that the mean of the principal
stresses a t timcs cxceeds p gh. The magnitude of this "tectonic overpressure"
is set: hy the strength of ,the racks .that support it.
A rough notion of how large thc overpressure may become may be obtained. from cz simplc model. Consiclcr a small spherical cavity in the Earth inside which he pressure is P, and suppose that h e stress clue to the weight of
t h c avcrlying rock is simply a hydrostatic pressure. In lhis case the stress diffcrence in the rock surrounding the cavity
. now
- is zero when P = p g l ~ We
calculate the largest vnluc of Pn = P -p g h allowed by the strength 01 the wall
rack. Pn can be iilcntificd with the maximum tectonic overpressure in that it is
the maximum mean stress h a t can be contained. No account of the origin of
his pressure is givm. It is assumed that tectonic Iorces do in Iact build up the
m a x i m u m tolerable prcssurcs, and that they are relieved by yielding of the
rocks, probably mainly in the vertical direction.
CC
-
648
Sydney
P. Clark, Jr.-A
Kedetern~ircc~tL)rr
If tile wall rock behaves as a perfectly plastic m a t c r i u l ~ ) l ) c ? ~
the
i nTrcwn
~
yield criterion (wllich in this case states [hat tile m a x i m u m slrrss diRwmc:c*
cannot exceed Y, the yield point ill simplo tension), ~ l l onmnirnmr p(~rmissil~lt*
value of Pn is (Hill, 1950, p. 104) :
Pa = 2 / 3 Y 1n ( E / 3 (1-a) Y ).
I$ Poisson's ratio, cr, is set equal to 1/3, and Y o L I ~ ~m' os( l ~ ~ l uIS',
s , is ~ n k c nt o
be 500 kifobars (Birch, Schairer, a n d Spicer, 1942) , I'N is fou~lclLo h c 3.7
kilobars if Y = 1 kilobar and 0.52 kilobars if Y = 0 . 1 . k i l o h r . 11: l h s ~ i c :flow
is not allowed in the wall rock, Pn = 2/3 Y, a rcsull: which i s itlanlicbnl t o ~ h t t
obtained by Birch (1955) Lrom a diflercnt argument.
Griggs, Turner, and Heard (1960) hove o t m x v r i l tcusilc slrrligtlls grrntt+r
than 1 kilobar in several rocks at 5 kilobars confining i,rassurrh and 800°C. AS
these authors are careful 1.0 point out, however, the cqwrirnc:rl~nlrtb..;dtsr d r r
to rates of strain that may exceed those occurring in mLurc? by a IILI*LOI*
US
large as 1012. This implies that the s ~ r e n g t h so f i-or:ks rnuy 1)c: suhstantinlly
smaller under natural conditions than under tlm conditions 06 L l ~ c wInljorulrsr'y
~
tests. This problem is complica~eclby recrystallization. The: sirrngth oI n rock
under natural conditions may Le ckterrni~icdby the rclulivch raltks of c'lcforrnntion and recrystallization.
An overpressure persisting lor only a few tlmusnntl ywrs, a lirrm tlrnl is
short geologically speaking, could significantly aReot tllo mincralogy c ) l ~ 1 1 1 *
rock. A value of Y of a few hundred bars might persist for short limcs during
active deformation; this leads to overpressures n I Z kilolrar or rnorc8, S i n w J
kilobar corresponds to the weight of nearly 4, km oE c~vesl~urt?c?n
in 111~c:ruwt,
the reduction in the depth of burial required may lm cmxsidarnlrln.
Evidence of 111e existence of tectonic overpressxxrcs i.n sor:ks, o t h r t I ~ 11
R
the fact that deformation takes place, is usually indefinite. No c:lcarcnt d i s ~ i n c t tion between tectonic pressure and deep burial can be rnaclo i n most regionally
metamorphosed terrains, because no way of dr.terminiiig dctptll irliivy~c!t~tXcntIy
of pressure has been found. Estimates based on t1iicknt:ss o S strata arc: vitialrv4
by tectonic thickenings and tliinnings oP unknown m u y n i t n d c . Although d i s torted crystals of kyanite are common, they only s h o w ~llatclc~lormntion folhwed growth. It may also have accompanied it, but thim: is no proof of iliir.
An unusual local occurrence of kyanite is i n the c o n t a c t nureolos o l gmni~ic*
bodies i n SW Ankole. Combe (1932) noted that kyanite occurs i n 1 1 ~ :sc:llixls
only here they have been strongly delormed by the fcorcolul emplucnmcmt of
the granites.
The hypothesis of tectonic overpressures represents a retllrn to the strc*s?i
mineral concept of Harker but in modified form. I-Iarkrr supposc:d that L I ~ P
fields of stability of minerals were influenced by shear. Trhis idea has inllcn into disrepute in recent years, both on theoretical g r o u n d s (Vcrlxoc)gc:n, 1.951:
Macdonald, 1957) and because of the occurrence 01 stress miner& in rockg
that show little or no evidence of deformation (Miyashiro, 194.9, 1951).
tonic overpressures provide a different reason for L L sLress minerals7'
which are i n reality high-pressure minerals) to be associated with shear. In
the Present view, shearing stresses make possible an increased mean -principn1
rrc:cs-
~ l r o s sand bring high-prossurc rrlirlerals into their fields of stability at depths
whort! t h y w o d d wrrnnlly l w unstable at the prevailing temperature.
r i
1 ho r e d imin c l h c slrcss mincral concept is petrographic observation,
~ l t h o u g hl i a r k c r (1939) also cited the experimental evidence then available
in iis slip~.x)rt,r lllc omicc:pL is not he result of any single observation, but
ralllcr 11~:r e a d 1 01 u(x:ornola~(:dc?xpoxiencethat certain minerals, one of which
j s kyarrik, c:lri~rnotc:rinti~:tlllyoccur in strongly deformed rocks. Although
Hnrkrr's rspliunatiotl o I i t i s probaldy wrong, the association of kyanite with
o
r
i ~ ~ o n v ~ l ~ ccxisis.
~ l c s sAn ntiraclive Ieature of the hypothesis of tectonic: ovcr1)rcssurc.s is t h l i t provitlcs a natural explanation of some of the obsorvaLions h i l t lorlncd lhc basis of ihe stress mineral concept.
It cunnot, ol (:c)ursv, be inlcrrcd that all kyanite is produced in regions of
lectonic: ovc?xprcLssurc.Ccmsi~lerahloclcsptlis of burial are undoubtedly necessary
~ l l crough calculations used here to arrive at
as wc.11. 11 is highly clpsirnl)lc.
an uppw lirnil 10 l l l ~tw~olli(:O V C ~ ~ T C S S LbeI ~refined
~
and improved as experi01.1 he strcngth oS rucks accumulated. A be~terunderstanding of
rnentd da1.~1
lllc s~.~-cwc~s
u r d rnoverncnls 11mt have aflectecl the Earth's crust can emerge
from such work, L I ~ L this i s ulnnusl certain to advance our knowledge of orogenic: r ~ m m
l c l i t m o r p h i ~processes.
ACKNOWLEDGMENTS
h d c ~ h t c d10 T. N. Cliflord lor calling my attention to the kyanites of
Ankolo and to G, A, Chinrlcr lor rcading he manuscript and making numerous
snggcst ions which led k o its irnprovcment.
I
~1x1
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