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Time Scales of Crystal Fractionation in

Magma ChambersIntegrating Physical,

Isotopic and Geochemical Perspectives

JOURNAL OF PETROLOGY

C. J. HAWKESWORTH

S. BLAKE

P.EVANS

R. HUGHES

RECEIVED SEPTEMBER 21, 1999; REVISED TYPESCRIPT ACCEPTEDFEBRUARY 7, 2000

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INTRODUCTION

The rate of crystallization in mafic magmas takes

much longer than in more evolved magmas.

A simple heat balance model for an evolving magmachamber is used to make predictions of the time

scales for magma differentiation,which are compared

with geologic and isotopic constraints on the rates of

crystallization.

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PHYSICAL PRINCIPLES OF

COOLING AND CRYSTALLIZATION

Magma crystallizes as a result of cooling and

degassing.

The rates at which thermal energy is lost from

magma chambers maintains geothermal poweroutputs of 100 1000 MW.

The maximum amount of cooling can be estimated

equating power output (P) , to the thermal energy

lost from a fixed volume of magma(V) divided by the

cooling time (tcool).

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P= V(cT + L)/tcool.

is the magma density .

c is the specific heat capacity.

T is the temperature drop.

L is the latent heat of crystallization.

is the mass fraction of crystals grown at this temparature range.

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Useries isotopes

Uranium-238 is an emitter, decaying through

the 18-member uranium series into lead-206.

The intermediate isotopes of the chain that

have very short lives relative to their parents

,can be used to date rocks and minerals

formed within the last few hundred years.

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Radioactive decay equations

NND

0

multiply each side by elt substitute N=N0-D

t

eNNl

0

teNDN

l 00

t

eNND

l

00

)1(0t

eNDl

0NNe

t l

DNNet l

substitute N0=N-D

NNeDt l

)1( teND l

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N1 l1 N2 l2 N3

dN1dt l1N1

dN2dt l1N1 l2N2

dN3dt l2N2

Decay Chain Systematics:

Consider a 3-member decay chain:

Evolution of this system is governed by the coupled equations:

Note that at secular equil, 2d

0d

N

t

N2 (t) l1l2 l1

N1o e l1t el2t N2

oel2t

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234U Excess

The activity of (234U)excess decreases with time: 234234 234 0 tEx Ex

U U el

And excess 234U corresponds to the 234U not supported by 238U:

234234 238 234 0 238

( )

tU U U U e

l

And dividing through by 238U activity, we obtain:234

234 0 238234

238 2381

t

A

U UUe

U U

l

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230Th Deficiency

So we grow in 230Th due to decay of238U and excess 234U (in atom number):

234 230230 234234230 234

t to

Ex ExTh U e e

l ll

l l

And converting to activity, substituting formula for 234UEx

, dividing by 238UA,

and simplifying, we obtain:

230 234 230

234 0230

230

238 238

230 234

(1 ) 1 ( )t t t

A A

UThe e e

U U

l l ll

l l

*Or, more realistically, we measure (230Th/238U) and 234U/238U,

and iteratively find an age that satisfies both the measurements

made today. We then are calculating also 234U/238U initial.

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secular

equilibrium

secular

equilibrium

230Th-234U activity growth lines

For most samples:

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How can the age of crytallization be

determined ? Phenocrysts from the rocks are chosen to date

using these isotopes , as they are first fractionated

from the magma.

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Conclusions

In principle ,short lived isotopes offer a

powerful way to investigate the ages of the

ages of the crystals . The time taken for 50% fractional

crystallization in mafics in longer than that

of felsics.

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References

Principles of isotope geology by GUNTER

FAURE. http://www.wise-uranium.org/rup.html. http://www.ieer.org/fctsheet/uranium.html.

http://www.ead.anl.gov/pub/doc/natural-decay-

series.pdf.

Dickins .

Priciples of igneous and metamorphic petrology by

JOHN .D WINTER

http://www.wise-uranium.org/rup.htmlhttp://www.ieer.org/fctsheet/uranium.htmlhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ead.anl.gov/pub/doc/natural-decay-series.pdfhttp://www.ieer.org/fctsheet/uranium.htmlhttp://www.wise-uranium.org/rup.htmlhttp://www.wise-uranium.org/rup.htmlhttp://www.wise-uranium.org/rup.html

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Acknowledgements

Dr. Ravikant .

Dr. Tarun Dalai.

Anwar Qadri Moinuddin.(07MS batch).

presented by

Anvesh . M . Reddy(08MSo29).