Yardley, B.W.D. (1989) An Introduction to Metamorphic
Petrology . Harlow: Longman.
Winter, J.D. (2009) Principles of Igneous and Metamorphic
Petrology , 2nd edn. Upper Saddle River, NJ: Pearson
Figure 2.8): plagioclase 42.5%, diopside 25.5%,
nepheline (NaAlSiO 4 ) 15.0%, olivine 17.0%. (Note
that nepheline does not appear in Figure 2.8.) What
mineral would crystallize first from a melt corre-
sponding to this composition?
2.6 Refer to Figure 2.9 and its caption. In what propor-
tions must diopside and plagioclase crystallize
from melt b to drive its composition along the
cotectic curve (the arrow in Figure 2.9d)?
Calculate the compositions and proportions of
the phases present in a solid mixture of composi-
tion a (Figure 2.9b). What would be the equilib-
rium assemblage for this mixture at 1220 °C? What
would be the compositions and relative proportions
of the phases present?
2.7 Figure 2.10 below shows the ternary eutectic in the
system CaMgSi 2 O 6 (Di)-Mg 2 SiO 4 (Fo)-Mg 2 Si 2 O 6
(En) at a pressure of 20 × 10 8 Pa. To what depth in
the mantle does this pressure correspond? What
are the compositions (expressed as Di x Fo y En z
where x, y and z are mass percentages) of the first
melts to form as (a) the mixture M and (b) the
mixture N are heated through the solidus?
Sources of thermodynamic data for minerals
Berman, R.G. (1988) Internally-consistent thermodynamic
data for minerals in the system Na 2 O-K 2 O-CaO-MgO-
FeO-Fe 2 O 3 -Al 2 O 3 -SiO 2 -TiO 2 -H 2 O-CO 2. Journal of Petrology ,
29 , 445-522.
Holland, T.J.B. and Powell, R. (1998) An internally consistent
thermodynamic data set for minerals of petrological interest.
Journal of Metamorphic Geology , 16 , 309-43.
2.1 Applying the Phase Rule to the reaction shown in
Equation 2.5, discuss the variance of points X and
Y in Figure 2.1.1a (Box 2.1). Identify the degrees of
freedom operating at point X.
2.2 Why does ice floating on water tell us that the
melting temperature of ice will be depressed at
2.3 At atmospheric pressure (10 5 Pa), the following
reaction occurs at 520 °C:
CaMgSi 2 O 6 (Di)
Ca Al Si O iO
CaAl Si O
Melt + Di
2 3 2
Use the data below to plot a correctly labelled P-T
diagram for pressures up to 10 9 Pa.
J K − 1 mol − 1
10 − 6 m 3 mol − 1
Grossular (Ca 3 Al 2 Si 3 O 12 )
Quartz (SiO 2 )
Anorthite (CaAl 2 Si 2 O 8 )
Melt + Fo
Wollastonite (CaSiO 3 )
Mg 2 SiO 4
Mg 2 Si 2 O 6
2.4 Refer to Figure 2.5. Calculate the relative propor-
tions of melt and crystals produced by cooling a
melt of composition m to (a) 1400 °C, (b) 1300 °C,
and (c) 1230 °C. What are the compositions of melt
and plagioclase at these temperatures? (Assume
that equilibrium is maintained throughout.)
2.5 Plot the following rock composition in the ternary
Direction of decreasing
Te rnary eutectic
Figure 2.10 Simplified phase relations in the system
CaMgSi 2 O 6 (Di)-Mg 2 SiO 4 (Fo)-Mg 2 Si 2 O 6 (En) at a pressure
of 20 × 10 8 Pa (for Exercise 2.7).
CaAl 2 Si 2 O 8 -CaMgSi 2 O 6 -Mg 2 SiO 4 (see