Myron G. Best. Igneous and metamorphic 2003 Blackwell Science

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proportion such that the bulk composition, 50 wt.%

silica, is exactly that of the initial melt. Fractional

crystallization, in contrast, has yielded an additional

crystalline phase, cristobalite. This ﬁnal cristo-

balite  enstatite “rock” is silica-oversaturated,

whereas the ﬁrst crystals that precipitated—

forsterite—manifest an undersaturated system.

In the model Mg

SiO

-SiO

system, forsterite and

enstatite constitute a reaction pair that forms across

the peritectic. In real fractionating magmas containing

additional components, a reaction pair of olivine and

orthopyroxene is manifested as a reaction rim of the

latter on the former in a single grain. On a larger

scale, this reaction pair might be manifested in layers

of olivine-bearing rock overlain by orthopyroxene-

bearing rock in a layered maﬁc intrusion (compare

lower-left diagram in Figure 5.9). In evolving interme-

diate composition calc-alkaline magmas, a reaction re-

lation between clinopyroxene and melt produces

hornblende. Incomplete reactions of this sort create

hornblende reaction rims around anhedral, unstable

clinopyroxene in dioritic rocks (Plate II). At lower T,

hornblende may react with a more evolved melt to

yield biotite. Two or more reaction pairs might develop

in a fractionating multicomponent magma and consti-

tute a discontinuous reaction series. Many different re-

action series are possible in magmas, depending on

their bulk chemical composition and intensive vari-

ables.

Incongruent Melting. Crystallization of a melt that

contains 59.85 wt.% silica and 40.15 wt.% MgO—the

composition of enstatite—was discussed to illustrate

the principle of the reaction relation. In the reverse

sense, if crystals of pure enstatite are heated at 1 atm,

they are found to melt in an unexpected manner. In

contrast to the familiar congruent melting of ice to liq-

uid water of the same composition, incongruent melt-

ing of enstatite yields a liquid that is slightly more

silica-rich plus forsterite crystals at its melting point of

1557°C (Figure 5.8 and reaction 5.3). As more heat is

absorbed into the 59.85 SiO

-40.15 MgO system,

forsterite dissolves in the silicate liquid, and eventually,

at about 1600°C, melting is complete, ﬁnally yielding a

melt of the same composition as that of enstatite.

Rather than having a unique melting T point at some

particular P, as do albite, forsterite, diopside (Figure

3.8), and some other pure end-member minerals, pure

enstatite has a melting T range through which the sili-

cate liquid, which coexists with other crystals, has a dif-

ferent composition from the initial solid. As shown

later, all solid solution minerals also melt incongruently.

It may now be realized that any “rock” mixture of

diopside and anorthite crystals also melts incongru-

ently (except for the one unique eutectic proportion) in

Figure 5.4. The initial melt has a eutectic composition

regardless of the proportion of diopside and anorthite

crystals. The incongruent melting behavior of mineral

solid solutions and rocks has profound implications

not only for magma systems but for the whole Earth.

Incongruent melting has produced the global-scale

“differentiation” of the planet into a mantle and more

silica-rich, Mg-poor crust over the course of its 4.5-Gy

evolution. Small degrees of partial melting of the peri-

dotitic mantle of basically olivine and pyroxene has

generated more Si-rich, Mg-poorer partial melts form-

ing the crust.

Liquid Immiscibility. In the Mg

SiO

-SiO

system a

homogeneous high-T melt lying between 70 and

100 wt.% silica will split into two stable immiscible liq-

uids upon cooling below the convex upward solvus,

shown by a dashed line in Figure 5.8. For example, an

initial liquid at 2000°C that contains 80 wt.% silica

Crystal-Melt Equilibria in Magmatic Systems

Fo Fo + En

High

Low

Crystalline

products

SiO

(wt. %)

30 40 50

MgO (wt. %)

Melt composition

FRACTIONAL CRYSTALLIZATION

En + Cr

Decreasing T

Crystalline

products

SiO

(wt. %)

30 40 50

MgO (wt. %)

Melt composition

Liquid line

of descent

Liquid line

of descent

5.9 Crystals and liquids produced during equilibrium crystalliza-

tion (top) and fractional crystallization (bottom) of an initial

melt that contains 50 wt.% silica in the binary system

SiO

-SiO

at 1 atm. In the equilibrium process, forsterite

crystals appear in the initial stage of cooling and the ﬁnal crys-

talline products are forsterite plus enstatite in a proportion

whose bulk composition is exactly 50 wt.% silica. During frac-

tional crystallization, the crystalline products, which are shown

here as a hypothetical gravity accumulation, are forsterite, then

enstatite, and ﬁnally enstatite plus cristobalite with decreas-

ing T. The liquid line of descent on the MgO-SiO

variation

diagram resulting from fractional crystallization is more ex-

tended in composition than from equilibrium crystallization.

The increase in silica and decrease in MgO of the residual melt

during either mode of crystallization displayed here are com-

mon in many natural magmas.

splits into two melts at 1900°C; one contains 72 wt.%

silica and the other 96 wt.%. The less abundant,

more silica-rich immiscible melt will form as drops in

the mass of less siliceous liquid. Because of differing

densities, the two melts could eventually segregate

into contrasting horizontal layers in the gravity ﬁeld.

Subsequently, as the two immiscible melts cool below

1700°C, cristobalite precipitates from each, but in

greatly differing amounts, found from the lever rule.

It is a property of immiscible melts that the crystal-

line phases in equilibrium with each are the same,

but in different modal proportions. Liquid immisci-

bility appears to be rare in natural multicomponent

magmas.

5.4 CRYSTAL-MELT EQUILIBRIA IN

REAL BASALT MAGMAS

The two binary systems examined so far provide valu-

able insights into crystal-melt equilibria in simple,

model maﬁc systems. The effect of additional chemical

constituents, such as Al, Fe, and Na on the behavior of

real maﬁc magmas has only been hinted. Other binary

diagrams could be explored, as could three- and four-

component (ternary and quaternary) diagrams, which

are discussed at length in Morse (1980). Instead, at

this point as a “reality check” we consider crystal-melt

equilibria in two real basalt compositions. Although

these two basalts are real rocks composed of many

components, they are only two points in the wide com-

positional spectrum of all rocks (Figure 2.4). What has

been gained over the simple binary model systems by

an examination of real multicomponent systems is lim-

ited by their unique compositions.

5.4.1 Makaopuhi Basalt

Nature provided an especially instructive experiment

for petrologists in the 1965 eruption of Kilauea, a vol-

cano on the island of Hawaii, when lava partly ﬁlled

the small preexisting Makaopuhi crater to form a lava

lake. Soon after a hard crust developed on the lake,

U.S. Geological Survey petrologists drilled into its still

molten interior. Samples of magma were collected at

various depths in the lake and temperatures were mea-

sured with a thermocouple. Photomicrographs of thin

sections made of the quenched samples (Wright and

Okamura, 1977) clearly show the sequence of precipi-

tation of crystalline phases in this basaltic magma

(Plate III, Figure 5.10, and Table 5.1). Each sample is

presumed to represent an equilibrium assemblage (ex-

cept as noted later) of crystals and melt at the indi-

cated T near atmospheric pressure in a closed magma

system.

The liquidus of the Makaopuhi basalt lies just above

1200°C and the solidus is at about 965°C. Throughout

most of this 235°C range of crystallization between the

98 Igneous and Metamorphic Petrology

5.10 Crystal-melt equilibria of the Makaopuhi, Hawaii, basalt at

about 1 atm. See also color photomicrographs, Plate III. Tem-

peratures, measured in drill hole, and amounts of melt, deter-

mined in thin sections as glass, are indicated by horizontal line

segments and crosses; length of line segments indicates uncer-

tainty in measured values. Heavy curve is best-ﬁt line to data

showing how the amount of melt varies with T. Range of T

over which each mineral precipitated from the melt is shown

at the bottom. Approximate range of solid solution composi-

tions from high to low T is Fo 82 to 76 in olivine, Mg/Fe 1.2

to 0.36 in clinopyroxene, and An 71 to 30 in plagioclase. (Re-

drawn from Wright and Okamura, 1977.)

liquidus and solidus, pyroxene and plagioclase solid so-

lutions coprecipitate. In simple binary systems only one

pure crystalline phase precipitates from a melt until it

reaches a eutectic or peritectic, but with more compo-

nents in a natural magma, two or more crystalline solid

solutions can coprecipitate. The crystalline silicate

phase at the liquidus (the liquidus phase) is a Mg-rich

olivine that occurs as relatively large euhedral crystals

(Plate IIIa). At about 1180°C, much smaller, somewhat

darker clinopyroxene and colorless plagioclase crystals

begin to coprecipitate with olivine. With decreasing T,

increasing amounts of these three crystalline phases co-

precipitate. Although not visible in the photomicro-

graphs, plagioclases become more sodic and pyroxenes

and olivines become more enriched in Fe relative to

Mg: That is, the Fe/(Fe  Mg) ratio increases, as the T

of crystallization decreases. Olivines below 1100°C are

corroded and embayed into anhedral shapes and there-

fore were unstable in the melt. Had there been more

time during cooling of that level of the lava lake, the re-

sorption of olivine would have been complete. Resorp-

tion of olivine into the melt with falling T is like that

seen for some compositions in the simple binary system

SiO

-SiO

. This conﬁrms that the reaction relation

5.3 persists in natural maﬁc magmas, but only in those

of appropriate silica-saturated composition, that is,

tholeiitic basalts.

It is obvious from the changes in the color of the

glass in Plate III that the melt also changed composi-

tion as the T changed. From 1170°C to 1075°C the

glass becomes darker brown as a result of enrichment

of Fe and Ti in the residual melt. This enrichment was

created because the concentrations of these elements

are less in the crystallizing phases than in the bulk

magma. An accompanying enrichment of incompatible

Na, K, and P in the melt also occurred because the par-

tition coefﬁcient of these elements in the coprecipitat-

ing minerals is 1 (Section 2.5.1). Ultimately, at about

1070°C, the activity of ilmenite in the melt reached 1;

that is, the melt became saturated with respect to il-

menite and it precipitated, together with magnetite.

Consequently, Fe and Ti were removed from the melt,

thus causing the color of the glass to change from red-

brown to pale gray. At about 1030°C, the melt became

saturated with respect to the phosphate mineral, ap-

atite, which then precipitated. As the residual melt be-

came sufﬁciently enriched in Na and K near the solidus

temperature, alkali feldspar precipitated as thin rims

on earlier-formed calcic plagioclases.

5.4.2 Basalt Magmas at High Pressures and High

Water Concentrations

Crystal-melt equilibria of naturally occurring rocks can

be determined in the laboratory by using equipment

like that used for determination of simple phase dia-

grams. However, instead of mixtures of pure reagent

compounds, ﬁnely pulverized rock is the starting mate-

rial.

Figure 5.11 presents phase relations as a function

of P and T for a tholeiitic basalt, such as the one

listed in Table 5.1. Obviously, crystal-melt equilibria

are strikingly different for dry (water-free) and water-

saturated conditions. Relative to dry conditions, the

water-saturated liquidus and solidus are depressed

almost 600°C at 10 kbar (near the base of the aver-

age continental crust). Melting and crystallization oc-

cur over a much broader temperature range, about

400°C, in the water-saturated system, where amphi-

bole is stable over a wide range of P and T. The sta-

bility of this hydrous, aluminous phase suppresses

the stability of plagioclase, which is only stable near

the solidus at relatively low pressures in the water-

saturated system.

Figure 5.11 also reveals that mineral stability in

basaltic systems is strongly dependent on P. At P 

20 kbar, corresponding to depths greater than about

70 km in the upper mantle, any basalt system—wet or

dry—is dominated by clinopyroxene and garnet solid

solutions. The garnet contains a substantial proportion

of the pyrope end member (Mg

) but also Fe

and Ca. Elements normally sequestered in plagioclase

at low P, such as Ca, Na, K, and Al, occur in the high-

P clinopyroxene solid solution known as omphacite,

which contains a substantial amount of the jadeite end

member (NaAlSi

). Increasing P increases the activ-

ity of sixfold coordinated Al

at the expense of four-

fold Al

in aluminosilicate melts because the sixfold

coordination is a more compact, or smaller-volume, en-

tity. This stabilizes Al

-coordinated crystalline phases

such as garnets and aluminous jadeitic pyroxenes in

Crystal-Melt Equilibria in Magmatic Systems

Table 5.1 Bulk Chemical Compositions (wt.%)

and Modal Composition (vol.%) of Basalts Whose

Melting Relations Are Shown in Figures 5.10 and

5.11 and Plate III (Makaopuhi). Data from Wright

and Okamura (1977) and Green (1982).

IGH

-A

LIVINE

AKAOPUHI

HOLEIITE

SiO

50.24 49.93

TiO

2.65 1.34

13.32 16.75

1.41

FeO 9.85 11.40t

MnO 0.17 0.18

MgO 8.39 7.59

CaO 10.84 9.33

O 2.32 2.92

O 0.54 0.37

0.27 0.19

Total 100.00 100.00

MODE

Olivine 5

Pyroxene 51

Plagioclase 30

Fe-Ti oxides 9

Glass 5

Alkali feldspar trace

lieu of Al

-coordinated feldspars. With increasing P,

calcic, more aluminous plagioclases destabilize before

sodic, less aluminous plagioclases. These phase rela-

tions demonstrate why feldspars are crustal phases and

are not normally stable in the sub-continental mantle.

The dense (3.3–3.4 g/cm

) high-P rock made essen-

tially of red pyropic garnet and green omphacite

clinopyroxene (Appendix A) that is of basaltic bulk

chemical composition is called eclogite.

5.5 FELDSPAR-MELT EQUILIBRIA

Because nearly all magmatic rocks contain feldspar, it is

imperative that their fundamental phase relations be

understood. We begin with a discussion of the three

binary systems (Kf-An, Ab-An, Kf-Ab) and then as-

semble these into the feldspar ternary of the three-

component Ab-An-Kf.

In the two model binary systems already considered,

crystalline solids have ﬁxed compositions with no solid

solution between end-member components. On the

other hand, the binary plagioclase system (Ab-An) ex-

hibits complete solid solution between end-member

components NaAlSi

(Ab) and CaAl

(An)

whereas the other two binary systems exhibit only par-

tial mutual solubility. Feldspars serve as models for

other major rock-forming minerals that are also solid

solutions.

5.5.1 KAlSi

(Kf )-CaAl

(An) Binary System:

Limited Solid Solution

This system (Figure 5.12) resembles the CaMgSi

CaAl

system except there is a limited mutual

solubility between the K- and Ca-feldspar compo-

nents of just a small weight percentage. A slender,

wedge-shaped one-phase stability ﬁeld labeled Kf

(K-

feldspar solid solutions) lies along the left-hand T axis

and a similar stability ﬁeld labeled An

(anorthite solid

solutions) lies along the right-hand T axis. Above an

isotherm through the eutectic, the boundary line be-

tween these wholly crystalline ﬁelds and the two-phase

ﬁelds of liquid  Kf

and liquid  An

is the solidus

line. The solidus line converges with the T-axes at the

melting points of pure anorthite and K-feldspar.

For a magma system An

at 950°C, an isother-

mal tie line shows that crystals of An

are in equi-

librium with liquid An

. The lever rule indicates

that 64 wt.% of this system is crystals, 36 wt.% liquid.

With increasing T, the solubility of the KAlSi

com-

ponent in anorthite crystals decreases, from about 4

wt.% at 850°C to about 2 wt.% at 1100°C.

100 Igneous and Metamorphic Petrology

500 700 900 1100 1300 1500

100

120

Pl + Px + Ol + L

Pl + Ol + L

Pl + L

LIQUID

Dry liquidus

Cpx +

Grt +

solidus

Cpx + Grt +

Pl + L

Dry

Cpx +

Pl + L

Cpx + L

Ol + L

Ol +

Cpx +

Ol + Cpx + Pl + L

Amp +

Grt +

Cpx +

Amp +

Cpx + Pl

+ L

Amp + Cpx + L

Amp + Grt + Cpx

+ L

CRYSTALS

Cpx + Grt + L

Coesite

Quartz

Water-saturated solidus

Water-saturated liquidus

T (°C)

Depth (km)

P (kbar)

Pl + L

Cpx

+ L

5.11 Generalized crystal-melt equilibria in tholeiitic basalt. This is actually two diagrams, which have been superposed to emphasize the strik-

ing inﬂuence of water on liquidus and solidus temperatures and on crystalline phase assemblages. Equilibria in the water-free “dry” sys-

tem are shown by solid lines. Equilibria in the water-saturated system are indicated by dashed lines and shaded area. Quartz-coesite poly-

morphic transition is shown by dotted line. (Redrawn from Green, 1982.)

5.5.2 NaAlSi

(Ab)-CaAl

(An) Binary

Plagioclase System: Complete Solid Solution

At 1 atm, the plagioclase phase diagram for mixtures

of the NaAlSi

(Ab) and CaAl

(An) end-

member components (Figure 5.13) consists of a convex

upward liquidus and convex downward solidus be-

tween the melting points of pure anorthite and pure al-

bite. Within the univariant two-phase region, L  Pl

(liquid  plagioclase solid solutions), speciﬁcation of a

T uniquely ﬁxes the equilibrium compositions of both

liquid and crystals, given by the ends of an isothermal

tie line where it intersects the liquidus and solidus

loops, respectively. Alternatively, speciﬁcation of the

composition of one phase ﬁxes the composition of the

other, as well as T. The modal proportion of crystals to

liquid at any particular T depends on the bulk compo-

sition of the univariant system and can be determined

from the lever rule.

At any T within the univariant two-phase region,

L  Pl

, plagioclase solid solutions are always more

calcic (anorthitic) than is the coexisting liquid, which is

more sodic (albitic). For example, the ﬁrst crystals pre-

cipitating from a liquid An

have a composition of

. The progress of crystallization can be followed

by drawing a series of isothermal tie lines at decreas-

ing T. As T decreases, more plagioclase precipitates,

and it, as well as the liquid, become more albitic. The

liquid line of descent in the plagioclase system yields

more Na-Si-rich residual melts.

Any plagioclase of intermediate composition be-

tween pure end member Ab and pure An melts incon-

gruently with increasing T, yielding a liquid more al-

bitic and crystals more anorthitic than the original. For

example, initial melting of crystals An

yields liquid

whose composition is An

. As T increases, the melting

progresses, creating a larger proportion of liquid to

crystals, both of which become more enriched in

CaAl

, as may be seen by drawing a series of

isothermal tie lines at successively higher temperatures.

In a sense, the process involves an inﬁnite number of

incongruent melting steps. At 1425°C the last crystal to

be consumed, An

, is in equilibrium with a melt of the

original bulk composition, An

It may seem paradoxical that in a closed system

progressive crystallization makes both crystals and

liquid more albitic and both more anorthitic for pro-

gressive melting. This happens because the modal

proportions of solid and liquid solutions change sym-

pathetically and continuously with the concomitant

continuous changes in their compositions as T

changes. This phenomenon can be shown in the fol-

lowing hypothetical reaction, which is an example of a

mass-balance equation, for a system whose bulk com-

position is An

5.4 72.9 wt.% liquid An

29.2

 27.1 wt.% crystals An

70.3

at 1387°C

 80.6 wt.% liquid An

32.3

 19.4 wt.% crystals An

73.6

at 1400°C

Continuous Reaction Relations. In order for continu-

ous sympathetic changes in compositions and in ratios

of coexisting solid and liquid solutions to occur, con-

tinuous reaction relations must take place between

them as intensive variables (T in this case) continuously

change. Continuous reaction relations in which reac-

tants and products coexist over a range of T are to be

contrasted with the discontinuous (peritectic) reaction

relation at a unique, single T in the system Mg

SiO

. To maintain a constant state of equilibrium be-

Crystal-Melt Equilibria in Magmatic Systems

101

5.12 The water-saturated system KAlSi

(Kf)-CaAl

(An) at

5 kbar. The presence of a separate water-rich phase makes this

system ternary, but for our purposes the H

O component can

be ignored. At 1 atm this binary system is complicated by a

large stability ﬁeld of leucite (Problem 5.7), which is elimi-

nated at high-P and water-saturated conditions as shown here.

The symbol Or is commonly used to denote the KAlSi

component, but our use of Kf is a reminder that different

atomic structural forms of potassium feldspar exist; orthoclase

is only one of these. The subscript ss on the crystalline phases

An and Kf denotes solid solutions. (Redrawn from Yoder et

al., 1957.)

5.13 The binary system NaAlSi

(Ab)-CaAl

(An) at 1 atm.

(Redrawn from Bowen, 1928.)

tween crystals and melt in the NaAlSi

-CaAl

system there is an exchange reaction between coupled

ions

5.5 Na



4

 Ca

2

3

Exchange must occur by migration (diffusion) of these

ions across the interface between the melt and already

formed crystals as intensive variables change. Obvi-

ously, the larger the crystals to be modiﬁed in compo-

sition; or the more viscous the melt, which makes ions

less mobile; or the faster the change in intensive vari-

ables; or combinations of these conditions, the less

chance there is for equilibrium to be maintained in the

system.

Therefore, we would expect that perfect, reversible

equilibrium crystallization in the plagioclase system

would only occur under exceptional circumstances. In-

deed, this expectation is borne out by the rocks them-

selves; perfectly homogeneous plagioclases of uniform

composition throughout are rare in magmatic rocks.

Instead, compositionally inhomogeneous, or zoned,

plagioclases are far more common and result from

incomplete reaction relations during fractional crys-

tallization as intensive variables change. Before com-

plete reaction with the melt can occur by diffusional

processes additional crystalline material of different

composition precipitates. Then, before the melt can re-

act with that newly accreted crystalline material, chang-

ing conditions inhibit further reaction. As the process

continues, the melt never has a chance to equilibrate

fully with the whole crystal, which becomes zoned as

a result. Bowen (1928) referred to such zoned solid

solution crystals as well as accumulated crystals in a

plutonic mass as a continuous reaction series (Figure

5.14).

During perfect fractional crystallization of a liquid,

such as An

(Figure 5.14), each liquid fraction, iso-

lated from all previously precipitated crystals, is effec-

tively a new system with no knowledge of its prior his-

tory. Because of the lack of reaction, Na



4

ions

are conserved and Ca

2

3

ions depleted in a rela-

tive sense in the liquid. Carried to completion, perfect

fractional crystallization theoretically creates a residual

melt that is ultimately NaAlSi

, at which composi-

tion it precipitates pure albite (An

). Hence, the

crystalline products in this hypothetical example of a

continuous reaction series range from An

to An

Fractionating, evolving liquids and related crystals

progress toward more sodic and silicic and less calcic

compositions. It is worth emphasizing once again here

that fractional crystallization signiﬁcantly extends the

range of T over which crystals precipitate, as well as

extending the range of compositions of liquid and

solid solutions, relative to equilibrium crystallization

(Figure 5.15).

Continuous reaction relations occurred in the

Makaopuhi magma system as the melt reacted only

partially with previously precipitated olivine, pyroxene,

and plagioclase solid solutions. Though inconspicuous

to the naked eye in Plate III, continuous changes in the

chemical composition of these solid solutions are re-

vealed by microprobe analyses of the minerals in the

quenched lava lake samples. The two maﬁc silicates be-

come more Fe-rich at the expense of Mg and plagio-

clases become more NaSi-rich with decreasing T.

Inﬂuence of Other Components on the Plagioclase

System. Increasing P increases liquidus and solidus

temperatures in the plagioclase system by only several

degrees Celsius per kilobar. In contrast, addition of

other chemical components, especially water, to the

system depresses the liquidus and solidus by hundreds

of degrees (Figure 5.16). Addition of CaMgSi

(Di)

depresses anorthitic compositions but not albitic com-

positions, so that small changes in T yield large changes

in the equilibrium compositions of the coexisting melt

and crystals. Dissolved water not only depresses the

liquidus and solidus but in multicomponent real mag-

mas stabilizes more calcic plagioclase. For example, in

subduction zone basalt magmas that are typically more

water rich, crystallizing plagioclase is more anorthitic,

to An

90–95

, than is plagioclase in relatively dry mid-

ocean ridge basalt magma ( Johnson et al., 1994).

5.5.3 NaAlSi

(Ab)-KAlSi

(Kf )

Binary Alkali Feldspar System

Dry, or with only small concentrations of water at rela-

tively low P, this system is complicated by a large sta-

bility ﬁeld of leucite (KAlSi

), whose composition

cannot be expressed in terms of the components

Ab and Kf. However, at between 2 and 3 kbars under

water-saturated conditions the stability ﬁeld of leu-

cite disappears and the system becomes truly binary

(Figure 5.17). Solid solution is complete between the

NaAlSi

and KAlSi

components; the solidus and

liquidus form loops on each side of a minimum-melting

composition. This minimum resembles a eutectic, in

that evolved residual liquids move to it and there pre-

cipitate an alkali feldspar solid solution, about Kf

. At

 3 kbar (water-saturated conditions at 3 kbar)

any feldspar precipitated from a melt is a homogeneous

alkali feldspar solid solution. As any feldspar cools be-

low the solidus, its isopleth eventually intersects the

convex-upward solvus, below which the single feldspar

unmixes, or exsolves, under equilibrium conditions,

into two stable alkali feldspar solid solutions. For ex-

ample, at 600°C an initially homogeneous feldspar Kf

exsolves into a K-rich feldspar solid solution Kf

and

a Na-rich feldspar solid solution Kf

. The lever rule in-

dicates that their proportions are about 83 wt.% and

102 Igneous and Metamorphic Petrology

Crystal-Melt Equilibria in Magmatic Systems

103

Fractional

crystallization by

gravitative settling

(b)

5.14 Fractional crystallization in a plagioclase model magma system whose composition is An

. (a) The range of transient liquid and crystal

compositions during cooling of the magma is indicated by the double and thick black lines, respectively, along the liquidus and solidus.

(b) Stacks of crystals (a continuous reaction series) that are more albitic toward the top representing schematically the product of frac-

tional crystallization by gravitative segregation of crystals in a less dense melt. The same sort of sequence, but rotated 90°, could occur

by side-wall crystallization along the steep border of an intrusion, as more albitic plagioclases would precipitate into the intrusion.

(c) Schematic product of fractional crystallization resulting from incomplete reaction relations; zoned crystals are more albitic toward their

margins. All An values are arbitrary except for initial crystals, which are An

. (d) Normal compositional zoning in plagioclase under cross-

polarized light in gabbro, Skaergaard intrusion, Greenland. Twinned grain in center of view has been carefully oriented to show lighter

gray interference color in slightly more albitic rim. Very slow interdiffusion of NaSi and CaAl ions in plagioclase has not taken place to

erase its zoning. Adjacent pyroxene grain (black in extinction orientation) has experienced subsolidus exsolution by means of more rapid

diffusion of Ca-rich and Ca-poor phases, forming a “blebby perthitic” intergrowth (white) within the original homogeneous crystal.

"Perthitic"

pyroxene

Zoned

plagioclase

0 0.5mm

(d)

Fractional

crystallization by

incomplete chemical

reaction forming

zoned crystals

(c)

1000

1200

1400

1600

20 40 60 80 100

Wt. % CaAl

NaAlSi

T (°C)

(a)

L + Pl

LIQUID

17 wt.%, respectively. These two feldspars produced

by the exsolution process usually segregate within the

original crystal as thin subparallel lamellae, forming the

intergrowth known as perthite. At lower temperatures

the mutual solubility decreases, that is, the miscibility

gap widens, as the feldspar structure tightens, so that at

500°C, for example, Kf

and Kf

coexist at equilib-

rium. Perthitic intergrowths in volcanic rocks are gen-

erally not visible even with a microscope, because the

magmas cool so quickly that the diffusion-controlled

exsolution does not create visible lamellae; these ex-

ceedingly ﬁne, cryptoperthitic intergrowths can, how-

ever, be discerned by X-ray diffraction analysis. Per-

thite is commonly visible in more slowly cooled plutonic

rocks, even with the naked eye. Sluggish rates of diffu-

sion within the crystal that preserve metastable compo-

sitions prevent the use of perthites as a geothermometer,

but they do furnish information on cooling rates.

At higher pressures, such as 5 kbar, in water-

saturated systems the solidus loop is depressed so far

that it intersects the solvus, forming an isothermal

boundary line between the two-feldspar and liquid 

feldspar ﬁelds (Figure 5.17b). In this case, the mini-

mum in the liquidus is a eutectic. The phase diagram

now resembles the Kf-An diagram (Figure 5.12), ex-

cept that the extent of solid solution between the two

end members is greater in the alkali feldspars. Starting

liquids that lie between about Kf

and Kf

and crys-

tallize in the equilibrium manner, as well as liquids of

any composition undergoing extreme fractional crystal-

lization, ultimately yield two feldspars, Kf

and Kf

Each of these phases may subsequently experience

slight exsolution upon cooling below the solvus.

The contrasting phase relations depicted in Figure

5.17 prompted Tuttle and Bowen (1958) to classify

granites into two textural categories, hypersolvus and

subsolvus (Figure 5.18). Hypersolvus granites, and

some syenites, crystallize from relatively dry magmas

whose phase relations are governed as are those in

Figure 5.17a where the chief or sole feldspar is

perthite; accompanying maﬁc minerals are commonly

anhydrous. Subsolvus granites and other felsic rocks

have two distinct feldspars that crystallize directly

from the melt (Figure 5.17b); accompanying maﬁc

minerals are commonly hydrous amphiboles and bi-

otite.

5.5.4 KAlSi

(Kf )-NaAlSi

(Ab)-CaAl

(An)

Ternary Feldspar System

The ternary feldspar system is of paramount impor-

tance in petrology because most rocks contain ternary

feldspar solid solutions. It also serves as an introduc-

tion to “reading” ternary phase diagrams. For realism

and for hastening of reaction rates, laboratory studies

of feldspars have involved water, making the system

quaternary. However, to keep the discussion simple,

water pressure is assumed constant and can be ignored

in an isobaric diagram.

104 Igneous and Metamorphic Petrology

1000

1200

1400

1600

20 40 60 80 100

Wt.%

T (°C)

LIQUID

L + Pl

Equilibrium crystallization

produces homogeneous

crystals An

CaAl

NaAlSi

5.15 Equilibrium crystallization in a plagioclase model magma sys-

tem whose composition is An

40.

The ﬁnal products of equilib-

rium crystallization are homogeneous crystals An

40.

600

800

1000

1200

1400

1600

20 40 60 80 100

NaAlSi

Wt. % CaAl

T (°C)

LIQUID

1 atm

+ Di

5 kbar

water-saturated

+ Quartz, 5 kbar

water-saturated

5.16 Comparison of liquidus and solidus temperatures in the pla-

gioclase system at 1 atm with projected liquidi and solidi

curves in systems with additional components. (Redrawn from

Johannes, 1978.) Dashed curves labeled Di are for a system at

1 atm in which diopside coprecipitates. (Redrawn from Morse,

1980.)

In ternary phase diagrams, T varies along an axis

perpendicular to an equilateral triangle on which are

represented the proportions of the three components

(review Figure 2.3b), in this case Kf, Ab, and An. Thus,

the four intensive variables T, X

, X

, and X

form

a triangular prism whose three side faces are the three

binary feldspar systems in Figures 5.12, 5.13, 5.17, and

5.19a. The upper bounding surface of the prismatic

volume (Figure 5.19b) is the liquidus surface, above

which, at higher temperatures, any mixture of compo-

nents is liquid. This three-dimensional liquidus surface

is analogous to the familiar topographic surface of the

Earth in that it has hills and valleys whose exact con-

ﬁguration can be represented by isothermal contour

lines drawn on the surface. A contour line on the liq-

uidus surface is the intersection of an isothermal plane

Crystal-Melt Equilibria in Magmatic Systems

105

5.17 The NaAlSi

(Ab)-KAlSi

(Kf) system under water-saturated conditions at 3 and 5 kbar (0.3 and 0.5 GPa). Granite magmas crys-

tallizing under conditions like those in (a) yield hypersolvus textures, whereas in (b) they yield subsolvus textures (Figure 5.18 and Plate

IV). Dashed lines in (a) are inferred liquidus and solidus where experimental data are lacking. Subscript ss refers to solid solutions. (Re-

drawn from Yoder et al., 1957; Morse, 1970.)

Perthite

Quartz

Perthite

(a)

Myrmekite

Plagioclase

(b)

K-rich

feldspar

5.18 Textural types of granites formed at contrasting water pressures during crystallization. Photomicrographs of thin sections under cross-

polarized light. (a) Hypersolvus granite formed under conditions like that in Figure 5.17a where only one initially homogeneous alkali

feldspar precipitated from the melt. This single phase subsequently unmixed at temperatures below the solvus from perthite, an inter-

growth of Na-rich and K-rich alkali feldspars. Associated maﬁc minerals are commonly anhydrous: Fe-rich pyroxenes and olivines.

(b) Subsolvus granite formed under conditions like that in Figure 5.17b, where two discrete feldspars—a sodic plagioclase and a potas-

sic alkali feldspar—coprecipitated from the melt; each may experience slight unmixing at lower temperatures, but this may not be obvi-

ous under the microscope. Associated maﬁc minerals are typically hydrous: biotite and amphibole. Turbid appearance of alkali feldspar

is caused by clay alteration and possible minute ﬂuid inclusions. Myrmekite is a vermicular intergrowth of quartz and sodic plagioclase.

106 Igneous and Metamorphic Petrology

KAlSi

NaAlSi

CaAl

(a)

5.19 The system KAlSi

(Kf)-NaAlSi

(Ab)-CaAl

(An)-H

O at moderately high P appropriate to shallow plutonic conditions.

(a) Three binary systems shown in previous ﬁgures are linked around a compositional equilateral triangle in which proportions of the

three components CaAl

, KAlSi

, and NaAlSi

are represented. The binary Kf-An system has been slightly distorted for clar-

ity. Points A, O, S, V, and so on, refer to points in subsequent ﬁgures of this ternary system. (b) Perspective view of the three binary sys-

tems folded up to form a three-dimensional triangular prism whose axis represents T. The underlying solidus and solvus surfaces

(Figure 5.20) have been omitted for clarity. The upper surface of the prism is the liquidus surface in three-dimensional T-X space on

which curved isothermal contour lines are drawn parallel to the compositional base of the prism. One isothermal plane (shaded) paral-

lel to the base is shown cutting the liquidus surface along isothermal contour lines on each side of the two-feldspar-liquid boundary line,

. This line lies in the thermal valley of the liquidus surface in which falling T is toward M

. The liquidus phases to the left of the

boundary line are plagioclase solid solutions; these coexist stably with any melt on this part of the liquidus surface. The liquidus phases

to the right of the boundary are alkali feldspar solid solutions. Melts lying on the boundary are in equilibrium with both feldspar solid

solutions. The end point of the boundary line does not lie on the NaAlSi

-KAlSi

join, but within the ternary with a small amount

of dissolved CaAl

. (See Nekvasil and Lindsley, 1990; Brown, 1993, for a discussion of the complexities at the termination of the

boundary line.) (c) Projection of isothermal contour lines and boundary line EM

from the triangular prism in (b) onto its base.

CaAl

NaAlSi

KAlSi

+ liquid

alkali

feldspar

+ liquid

Isothermal

plane

(b)

L + Pl

L + Kf

(c)