MINERALOGICAL SOCIETY OF AMERICA, SPECIAL PAPER 1, 1963INTERNATIONAL MINERALOGICAL ASSOCIATION, PAPERS, THIRD GENERAL MEETING

EFFECTS OF THE CHANGES IN SLOPE OCCURRING ON LIQUIDUS AND SOLIDUSPATHS IN THE SYSTEM DIOPSIDE-ANORTHITE-ALBITEI

PETER J. WYLLIE

Department of Mineralogy, The Pennsylvania State University, University Park, Pennsylvania

ABSTRACT

Liquidus and solidus paths in the system diopside-anorthite-albite exhibit changes in slope. When plagioclase crystal-lizes alone from a ternary liquid both paths are steeper than in the system anorthite-albite, but when plagioclase is joinedby diopside both paths become much less step than in the binary system. This fact, together with other evidence, suggeststhat the liquidus profile of an igneous rock series may be characterized by three shelves (where small temperature changescause much fusion or crystallization, and large compositional changes) separated by steep slopes (where large temperaturechanges cause little crystallization or fusion, and small compositional changes). The shelves extend across picritic composi-tions (upper), basic and intermediate compositions (middle), and acid compositions (lower). The changes in slope may helpto account for the relative proportions of various igneous rocks in different petrographical associations. The origin of pri-mary basaltic and intermediate magmas, and the rarity of intermediate rocks in basic-acid igneous associations are dis-cussed. Marginal zoning, oscillatory zoning, and the development of two generations of crystals (with continuous cooling)are discussed in terms of changes in slope of solidus paths.

INTRODUCTION

During the fractional crystallization of basalticmagma, the composition and behavior of early pre-cipitates of olivine, plagioclase feldspar, and pyrox-ene are important in determining the compositionand amount of later differentiates. Concepts ofbasaltic differentia tion have therefore been influ-enced by the phase diagrams for the systems for-sterite-fayalite (Bowen and Schairer, 1935) andanorthite-albite (Bowen, 1913). Each system formsa complete series of solid solutions, with melting in-tervals at temperatures intermediate between themelting points of the end members, and the liquidusand solidus curves form simple loops with no abruptchanges in slope. This simple pattern, of course, doesnot persist in more complex systems. Addition ofCa2Si04 to the system forsterite-fayalite produces anextensive shelf on both liquidus and solidus surfacesof the orthosilicate plane (Ricker, 19522). Possibleeffects of this shelf, if it persists in the naturalperidotite-basalt system, were discussed in an earlierpaper (Wyllie, 1960; Buddington pointed out, in con-versation, that the term "plateau" used in this paperto describe the gently sloping areas on the liquidusand solidus surface is inappropriate, and the term"shelf" is now adopted). Examination of Bowen's(1915) results in the system diopside-anorthite-albitereveals that addition of diopside to the system

1 Contribution No. 61-27 from the College of Mineral Industries.2 The solidus surface must be intersected by a solvus between

the forsterite-fayalite and the monticellite-kirschteinite series,and this certainly contributes to the shelf feature on the solidus,which is indicated by Ricker's preliminary data.

anorthite-albite produces a pattern of slopes forliquidus and solidus paths which is rather similar tothat produced by addition of Ca2Si04 to the system'fors teri te-fayali teo

LIQUIDUS AND SOLIDUS PATHS

Equilibrium and fractionation liquidus paths havefrequently been discussed in geological literature, butsolidus paths have received less attention. Liquidusand solidus paths illustrate the compositional changesof coexisting liquids and crystals with increase or de-crease in temperature. If a path is steep, large tem-perature changes produce small compositionalchanges, whereas if a path crosses a gently slopingshelf, small changes in temperature produce largecompositional changes.

In each of the binary systems forsterite-fayaliteand anorthite-albite there is one liquidus path andone solidus path, and their slopes change continu-ously from one component to the other. In a multi-component system there are many liquidus pathswhich vary with the composition of the initial liquid(crystallization processes) or crystalline mixture(fusion processes), and with the degree of fractiona-tion. For each liquidus path there are several soliduspaths giving the compositions of minerals in equi-librium with the liquids at various temperatures.With decreasing temperature the minerals may beprecipitated or resorbed. An example of the lattersituation is offered by the reaction relationship ex-hibited by olivine in many silicate systems and insome basic magmas. A discontinuity occurs in theslope of liquidus and solidus paths whenever a phase

204

DIOPSIDE-ANORTHITE-ALBITE SYSTEM 205

appears in or disappears from the system. In manysystems, rather abrupt changes in slope occur with nochange in the number of phases.

A certain amount of supersaturation is required toinitiate crystallization of most liquids, and theamount required depends upon the properties of theliquid and crystals. A moderate degree of supersatura-tion in silicate magmas probably leads to the pre-cipitation of a few crystals which attain large sizes.If crys talliza tion is ini tia ted at a higher degree ofsupersaturation the number of crystals precipitatedincreases markedly but they remain small (Turnerand Verhoogen, 1960, p. 47). When a liquidus path issteep the liquid temperature must fall quite far belowthe liquidus to produce much supersaturation, butwhen the slope is gentle a high degree of supersatura-tion can be produced if the liquid temperature fallsonly slightly below the liquidus.

The nature of the continuous zoning developed inminerals depends upon many factors, including theslope of the solidus path for the mineral. If thesolidus path is steep the compositions of successivezones change only slightly even in large temperatureintervals, but if the slope is gentle a wide range ofzoning can be developed in a small temperature in-terval.

THE SYSTEM DIOPSIDE-

ANORTHITE-ALBITE

The main features of this system are summarizedin Figs. 1 and 2, and a comprehensive account ofequilibrium and fractional crystallization for variousliquids has been presented by Bowen (1915). It isnow known that the phase relationships are more

Di1600

B1500

Ab

Ab 20 40 60 80 AnWEIGHT PER CENT

An

FIG.1.The systemdiopside-anorthite-albite, after Bowen (1915).A. Three-phase triangles measured by Bowen.B. Perspective TX projection of the solidus and the liquidus

field boundary. Three-phase triangles project as horizontallines connecting pairs of points on the field boundary andsolidus. The liquidus and solidus for the system anorthite-albite are shown as dashed curves (Bowen, 1913).

1600 1600

Ab 20 40 60 80 An Ab 20 40

WE IGHT PER CENT

60 80 An

Fig. 2. Equilibrium crystallization in the system diopside-anorthite-albite.

A. Crystallization of liquids D and E, after Bowen (1915). Forexplanation see text and Bowen's paper. The open circle isthe projected composition of Nockold's (1954) average"central" basalt (see text and Fig. 3).

Band C. Perspective TX projections of the liquidus and soliduspaths for the liquid D (DPMH and AGSF) and for theliquid E (ERNO and BKTL) in Fig. 2A. With fractionalcrystallization, these paths would continue down the heavydashed curves to C. The liquidus and solidus for the systemanorthite-albite are shown as light dashed curves.

complex than indicated, because appreciable substi-tution of alumina occurs in the pyroxene (Hytonenand Schairer, 1961). Schairer and Yoder (1960) haveshown that there is no eutectic on the join diopside-albite, but that the point labeled C in Fig. 2 is apiercing point at a considerable higher temperature,1133° C. However, revised data for the whole systemare not available, and it will be assumed in the fol-lowing discussion that the system remains ternary.Since most of the compositions considered lie in theplagioclase field, departures from ternary behaviorprobably have little effect on the general pattern ofcrystallization.

Each liquid on the field boundary coexists withdiopside and a plagioclase feldspar of fixed composi-tion, and the three phases coexisting at each tem-perature are represented by the corners of a three-

206 PETER J. WYLLIE

phase triangle. Those experimentally measured byBowen are illustrated in Fig. 1A. During crystalliza-tion, the liquid and the plagioclase feldspar are en-riched in albite relative to anorthite. The extent ofthis enrichment is indicated by the ratio of albite/anorthite (Ab/An), and it is illustrated in Fig. 1B, aprojection of the field boundary and of the solidusfrom within the TX prism on to the An-Ab- T face ofthe prism. The three-phase triangles project as linesconnecting pairs of points on the field boundary andthe solidus. The proportion of diopside in the liquidis not represented because the projection is madehorizontally through the diopside- T edge. Liquidusand solidus boundaries for the system anorthite-albite (Bowen, 1913) are plotted for comparison.Ternary crystallization temperatures are lower and,except near albite, the projected ternary field bound-ary and the solidus both slope much more gently thanin the binary system. The difference in compositionbetween coexisting liquid and plagioclase in terms ofthe ratio Ab/ An is smaller in the ternary system thanin the binary system. This is also true for plagioclaseprecipitated from multicomponent magmatic liquids(Wager, 1960a, Fig. 12).

Addition of other components to the system, inmoderate amounts, would cause the field boundaryto generate a surface with the form of a shelf. Theboundary is only a line passing across this shelf, but,for convenience, whenever this feature appears on aliquidus or solidus path it will be referred to as ashelf.

Bowen described the equilibrium crystallization ofthe mixtures D and E in Fig. 2. The liquid D followsthe path DPMH while the plagioclase changes com-position from A to F, and the liquid E follows thepath ERNO while the plagioclase changes from B toL. The enrichment of liquid and plagioclase in theratio Ab/ An is illustrated by the liquidus and soliduspaths in Figs. 2B and C. These diagrams were ob-tained in the same way as Fig. 1B, by projecting thetie-lines for coexisting liquid and plagioclase.Liquidus and solidus paths in the binary plagioclasesystem are plotted for comparison. When plagioclasecrystallizes alone from a ternary liquid the projectedliquidus and solidus paths are steeper than in thebinary system, but as soon as plagioclase is joined bydiopside they become less steep than in the binarysystem. It should be noted that the slope of a pro-jected liquidus path is not the same as its actualslope on the liquidus surface. However, although theslopes of the paths DPM and ERN are not quite assteep as indicated in the projection, they are steeper

than the slopes in the binary system during the corre-sponding composition intervals (compare Figs. 2A,2B, 2C).

The slopes of the liquidus paths in these projec-tions may be considered as measures of differentia-tion of the liquid. The steep slopes DM and EN indi-cate that little differentiation occurs while plagioclasealone crystallizes from a multicomponent liquid,whereas the gentle slopes MH and NO indicate thatwhen plagioclase is joined by other crystalline phasesmuch differentiation occurs in a small temperatureinterval.

The influence of the slopes of liquidus paths on therate of crystallization of liquids is demonstrated byBowen's data for the liquids D and E (Fig. 2A).Liquid D begins to crystallize at 1,3750 C., and ap-proximately 50% crystallizes while its compositionchanges from D to M in a temperature interval of1590 C. The remaining 50% crystallizes while itchanges composition from M to H in a temperatureinterval of only 160 C. Similarly, approximately 75%of liquid E crystallizes along the path EN in a tem-perature interval of 2350 C. and the remaining 25%crystallized along the path NO in a temperature in-terval of only 80 C.

Bowen also discussed fractional crystallization inthis system. Continuous zoning of the plagioclaselowers the temperature of final consolidation, andcauses enrichment of the liquid, and of the outerplagioclase zones, in the ratio Ab/ An. The liquids Dand E then follow paths similar to those illustrated inFigs. 2B and C, with two modifications. The liquiduspaths DPM and ERN, and the solidus paths AGSand BKT become somewhat less steep, joining theprojected field boundary and solidus at temperatureslower than those indicated by MS and NT. However,Bowen's diagrams confirm that the paths for thesecompositions remain steeper than the correspondingpaths in the binary system. The final liquid persiststo much lower temperatures than indicated by HFand OL, and with strong fractionation the lateliquids, and the outer plagioclase zones, could con-tinue to the point C, the albite-diopside eutectic(assuming, for convenience, that the albite-diopsidejoin remains binary).

Fusion processes can be traced by following theliquidus and solidus paths in the direction of in-creasing temperature. Partial fusion of the crystallinemixtures D and E, composed of diopside and homo-geneous plagioclase feldspar, produces first a trace ofliquid with compositions Hand 0, respectively. Be-cause these liquids lie on the shelf, small increases of

DIOPSIDE-ANORTHITE-ALBITE SYSTEM 207

temperature are followed by considerable melting asthe liquid changes composition up the gentle slope ofthe shelf. Once the liquid leaves the shelf (at M andN respectively), much larger temperature increasesare required to cause much further melting or changein liquid composition. For example, if equilibrium ismaintained, an increase in temperature of 160 C. issufficient to melt 50% of the mixture D while theliquid changes from H to M, but a further increase of1590 C. is required to melt the remaining 50%. Evenif equilibrium is not maintained, i.e. if the crystallineplagioclase fails to react continuously with the liquiddeveloped, the general pattern is unchanged. If themixture D is composed of diopside and zoned plagio-clase crystals, the first liquid developed is richer in theratio Ab/ An than H, and it forms at a lower temper-ature.

HAPLOBASALTIC, HAPLODIORITIC AND

HAPLOGRANITIC MAGMAS

The compositions of many igneous rocks can berepresented approximately in the system diopside-anorthite-albite-orthoclase-silica. Bowen (1915)pointed out the close chemical and mineralogicalcorrespondence of some natural basalts and dioriteswith mixtures lying close to the field boundary inthe system diopside-anorthite-albite. The assem-blages labradorite-l-diopside and andesine-l-diopside,with bulk compositions lying close to the field bound-ary, he called haplobasaltic and haplodioritic, re-spectively. Liquids with these compositions weresimilarly called haplobasaltic and haplodioriticmagmas. Haplogranitic compositions lie close to thesystem albite-orthoclase-silica, but if these composi-tions are projected from within the five-componentsystem onto the system diopside-anorthite-albite,with orthoclase-l-albite-l-silica plotted jointly asalbite, they are represented by points not far removedfrom the field boundary in the system diopside-anorthite-albite. Therefore, although the assemblagealbite-l-diopside (with bulk composition close to thefield boundary) is not closely related in compositionto granites, it is considered useful in this review to re-fer to this assemblage as haplogranitic. The assem-blage oligoclase-l-diopside can be referred to ashaplogranodioritic. These terms are used in Fig. 3.

It is often stated that typical basalts are composedessentially of labradorite and pyroxene, and thatthese minerals begin to crystallize almost simultane-ously (Bowen, 1928, pp. 64-69; Hess, 1960, p. 178).This has been demonstrated experimentally for somebasalts by Yoder and Tilley (1957). Such basalts are

1400

w 1300rr::Jt--<!n::wQ._ 1200::;;:wt--

1100

WEIGHT PER CENT

FIG. 3. Perspective TX projection of the liquidus and soliduspaths (ACE and BDF) for equilibrium crystallization of the felds-pathic haplobasaltic magma, A, representing the "central"basalt projected onto Fig. 2A. With fractional crystallization thepaths would continue down the heavy dashed lines to G (thelettering in this figure does not correspond to that in Fig. 2). Theliquid compositions on the path ACEG are related to their nearestigneous equivalents by their designation as haplomagmas. Normalhaplobasaltic magmas lie on or close to the field boundary be-tween C and H.

described as "normal" in this paper to distinguishthem from what are here referred to as "olivine-,""pyroxene-," and "feldspar-basalts." "Olivine-ba-salts" precipitate olivine first, followed later byplagioclase and pyroxene. "Pyroxene-" and "feld-spar-basalts" first precipitate either pyroxene orplagioclase, respectively. Normal basalts correspondto haplobasaltic compositions lying on the fieldboundary in the system diopside-anorthite-albite.Pyroxene-basalts correspond to haplobasaltic com-positions lying in the diopside field, and feldspar-basalts correspond to haplobasaltic compositionslying in the plagioclase field. Nockold's (1954) aver-age "central" basalt is plotted in Fig. 2A in terms ofits normative pyroxene and plagioclase; it corre-sponds to a feldspar-basalt. Liquidus and soliduspaths for a haplomagma with the composition of thispoint in the system diopside-anorthite-albite (feld-spathic haplobasaltic magma) can be estimated fromBowen's (1915) data, and the result is shown in theprojection of Fig. 3.

The liquid (A) begins to crystallize at 1,3050 C.and, with equilibrium cooling, approximately 20%crystallizes in an interval of 700 C. (AC), while theplagioclase changes composition from about An84to An79 (BD). Plagioclase is then joined by diopside.The remaining 80% of the liquid crystallizes in atemperature interval of only 250 C. (CE) while the

208 PETER J. WYLLIE

plagioclase changes compositon to An59 (from D toF). The final liquid (E) at 1,2100 c., with a ratioAb/ An of 0.75, is haplogranodioritic in composition.With strong fractional crystallization, zoning ofplagioclase would cause the liquid to change com-position to G, reaching haplogranitic compositions.

In order to examine the final stages of crystal-lization of haplogranitic magmas it is necessary toconsider the effect of the additional componentsorthoclase and silica. Bowen (1928, pp. 104-110)briefly discussed the systems diopside-anorthi te-albite-orthoclase and anorthite-albite-orthoclase-silica in connection with the crystallization of basal-tic magma. Many parts of the complete five-com-ponent system have since been determined experi-mentally (cf. Schairer, 1957). The effects of addingmoderate amounts of the components orthoclase andsilica to mixtures corresponding to haplobasalticmagmas in Fig. 3 would be insignificant until thelater stages of fractional crystallization. (During themiddle and late stages of crystallization of naturalmagmas, the components of diopside in the syn-thetic system appear in hydrous phases such as

{OLIVINE -, PYROXENE-,

( AND FELDSPAR-BASALTS

IIIIw

a:::Jf-«a:wQ_

ZWf-

-, ....1- ......<,

I I'I "-I I ';----- _iOLIDUS <,.....~ I I I --------:::..

~I~ I« w I I I~ I ~ I ~ I INTERMEDIATE I ACID~ I u I « I I_J1a::1 CD I I::::> I I I

I I I IROCK COMPOSITIO N

FIG. 4. Possible liquidus and solidus profiles for an igneous rockseries. The liquidus profile represents one liquidus path throughmulticomponent space. The solidus profile does not represent asolidus path for any particular mineral. This tentative diagramillustrates schematically the temperatures of beginning of meltingand of complete melting for a series of igneous rocks.

amphibole and mica.) If Ab in Fig. 3 were replacedby albite-l-orthoclase-l-silica, the general pattern offractional crystallization would be similar to thatillustrated, except that the final temperature of con-solidation at G would be lower, the final liquids andfeldspar crystals would contain an appreciable pro-portion of K20, and quartz would be precipitated inthe closing stages of crystallization. All liquidus tem-peratures would be somewhat lower, increasingly sofor the more acid compositions. Final crystallizationof haplogranitic magmas would occur near thefeldspar-quartz field boundary of the Residua Sys-tem, and this stage may be represented by anothershelf on the liquidus surface.

LIQUIDUS SLOPES FOR IGNEOUS ROCK SERIES

Combination of extrapolations from Fig. 3 with theinferences discussed above and in the earlier paper(Wyllie, 1960) provides the liquidus profile illus-trated in Fig. 4. This is a tentative working modelrepresenting one possible liquidus path through themulticomponent system including all igneous rocks.The stage of differentiation can be represented by aparameter such as the differentiation index (Thorn-ton and Tuttle, 1960). The liquidus temperatures,the gradients of the slopes, and the positions ofchanges in gradient probably vary from one igneousseries to another. The effects of pressure, with orwithout volatile components, are considerable. Atemperature scale on Fig. 4 would thus be meaning-less unless for a specific suite of rocks under specificconditions. Thermal data of this kind are not yetavailable.

The liquidus profile illustrates the rate of changeof liquid composition for a constant rate of temper-ature change during the fractional crystallization of amagma, or the fusion of a crystalline igneous rock. Itshould be stressed that this representation need notimply that the rocks plotted have ever existed ascompletely liquid magmas. Shelves extend acrosspicritic compositions (ranging from olivine-richbasalts to peridotite), across the composition range ofbasic and intermediate rocks, and across acid com-positions. These will be referred to as the upper,middle, and lower shelves, respectively. They areconnected by steeper liquidus slopes.

Evidence for the existence of the middle shelf andthe steeper slope above it is reviewed in the precedingpages. Nockolds (1936) hinted at the possible exist-ence of a shelf feature for this compositional rangewhen discussing the rarity of intermediate magmasin basic-acid igneous associations. He suggested that

DIOPSIDE-ANORTHITE-ALBITE SYSTEM 209

perhaps the pyroxene and plagioclase crystallizedfrom a basic magma through a comparatively smalltemperature range, so that unless the residual magmawas removed during a comparatively short space oftime, intermediate rocks would not form.

Below the middle shelf, the liquidus slope for acidmelts appears to increase in steepness (Fig. 3). Theincrease may be only apparent in the system diopside-anorthite-albite, because the temperature of thepo in t G in Fig. .3 is now known to be 11330 C.(Schairer and Yoder, 1960). However, similarchanges in slope occur in several systems for com-positions corresponding to approximately the samestage of differentiation. In the systems leucite-forsteri te-silica, leuci te-diopside-silica, leuci te-anor-thite silica, and nepheline-anorthite-silica (illus-trated in Figs. 30, 31, 32 and 35 of Schairer's usefulreview paper, 1957) the field boundaries separatingthe primary fields of forsterite, enstatite, diopside andanorthite, respectively, from the primary fields of oneof the minerals of the Residua System, follow rathergently sloping paths at higher temperatures. Atlower temperatures, as the field boundaries approachthe Residua System, the slopes of the field boundariesincrease appreciably. This increase in slope occurswith no change in the number of coexisting phases.That the steep slope at the low-temperature end ofthe middle shelf (Fig. 4) does exist is therefore sug-gested by the pattern of crystallization exhibited byseveral synthetic systems.

The existence of a steep liquidus slope for residualacid melts has been inferred from petrological studies.Bailey et al. (1924) suggested that after the crystal-lization of the gabbroic minerals in the Glen Morering dike, there was "a marked pause in the processof crystallization" before the granitic residuumcrystallized. Holmes and Harwood (1928) suggestedthat after crystallization of the main part of tholeiiticsills, the residual acid liquid passed down a steeply-dipping groove in multi-dimensional space until itfinally crystallized as micropegmatite.

The crystallization of the final liquid as grano-phyre or micropegmatite may be compared with thecrystallization of liquids on the feldspar-quartz fieldboundary of the Residua System. From the data ob-tained by Tuttle and Bowen (1958, Fig. 23) it can beseen that, in a given temperature interval, much morecrystallization occurs when feldspar and quartzcrystallize together than when feldspar crystallizesalone. The final stages or crystallization of magmas,marked by the appearance of quartz, may thus berepresented by the lower shelf indicated in Fig. 4.

A steep liquidus for the composition range includ-ing feldspar-, pyroxene-, and olivine-basalts connectsthe middle and upper shelves. The steep slope forfeldspar-basalts is illustrated by AC in Fig. 3. A sim-ilar pattern is found for compositions correspondingto "olivine-basalts" in the system MgO-FeO-Si02(Bowen and Schairer, 1935). Few basalts containmore than a small excess of either plagioclase orpyroxene, and the compositional range of such ba-salts may be limited to the lower part of the steepslope just above the middle shelf. There is no similarlimit on the amount of olivine contained by crystal-line basalts and other basic rocks (although theremay be a limit on the amount of olivine contained insolution in basic magmas, as suggested by Bowen in1928), and the liquidus path thus continues up thesteep slope for rocks approaching picritic composi-tions. There are indications from the system CaO-FeO-MgO-Si02 that as the content of dissolvedforsteritic olivine increases in liquids of certain com-positions, at least, a steep liquidus gives way to ashelf feature. Possibly, therefore, the steep liquiduscorresponding to olivine-basalts may give way to anupper shelf for picritic compositions (Wyllie, 1960).For ultrabasic rocks above the upper shelf, liquidustemperatures are high and the slope is steep.

The dashed line in Fig. 4 is a possible solidus pro-file reflecting the liquidus pattern of shelves and steepslopes. It is not a solidus path for any particular min-eral.

Several liquidus profiles of this type for differentigneous rock series could be represented on a surfaceillustrating not only the stage of differentiation butalso the compositional variations between rocks atthe same stage of differentiation (e.g. between alka-line, calc-alkaline, and tholeiitic series). The problemlies in finding suitable parameters to separate thedifferent series (Wager, 1960b).

PETROLOGICAL ApPLICATIONS

The thermal regime of a magmatic system is com-plex. The rate of temperature change depends uponmany factors, in particular upon the heat balance be-tween the magma, the phases crystallizing from themagma or being dissolved by it, and the regional sur-roundings. Most of these factors cannot be evaluatedbecause insufficient thermodynamic data are avail-able. For simplicity, therefore, the preliminary petro-logical applications which follow refer only to a con-stant rate of temperature change. It is unlikely thatthese conditions ever obtain in natural systems, butthe conclusions reached by making this assumption

210 PETER J. WYLLIE

will serve as working hypotheses. It should be bornein mind that although only small changes of tempera-ture are required to cause considerable melting orcrystallization of compositions on shelf features, theamount of heat involved is much larger than for cor-responding temperature intervals on steep liquidusslopes. The latent heat of fusion is an important itemin the thermal budget.

Applications of two types may be considered: (a)changes in the slope of liquidus paths in igneous sys-tems may help to account for the relative proportionsof various igneous rocks in different petrographicalassociations, and (b) the nature of continuous zoningin minerals will be dependent on changes in slope oftheir solidus paths.

Primary basalts. Basalts may be formed by partialfusion of feldspathic peridotite (Bowen, 1928). Theintermediate magma first developed on the middleshelf (Fig. 4) increases rapidly in amount while itchanges composition up the gentle slope of the shelf.Basaltic magma is formed at the high-temperatureend of the shelf and on the lower part of the steepslope above it. A similar pattern would persist if thecrystals involved were the high pressure phases(Yoder and Tilley, 1961). Garnet, clinopyroxene, andolivine would melt together while the liquid changedcomposition across the shelf, and when only liquidplus olivine remained, the middle shelf would giveway to a steep slope, as illustrated in Fig. 4. Both therate of fusion and the rate of change of composition(for a constant rate of temperature increase) decreasemarkedly when the steeper slope above the shelf isreached. This change in slope might well be a vitalfactor in limiting the products of fusion to the chem-ical composition of primitive basaltic magmas.

Ultrabasic magmas. If ultrabasic magmas are everformed their composition may similarly be limited bythe steep liquidus rising above the upper shelf (Fig.4). The behavior of picritic magmas, which wouldlie on the upper shelf if they exist, was discussed inthe previous paper (Wyllie, 1960).

Primary intermediate magmas. Partial fusion of sialicrocks in the earth's crust initially yields an acid melt.Its composition and the amount developed dependupon the bulk composition and mineralogy of thesialic rocks. When the temperature exceeds the thresh-old of the middle shelf (Fig. 4), rapid melting followswith the formation of large amounts of intermediatemagma. If the original acid melt has not previously

been separated from the rock this is incorporated inthe magma. It changes composition rapidly up thegentle slope of the shelf, but its composition is limitedby a steep liquidus path rising from the shelf, theexact position of which depends on the composition ofthe rock being fused. By the time this stage is reached,most sialic rocks would contain only a small residueof crystalline material. Other crustal rocks, more basicin composition, or containing an excess of aluminousminerals compared to compositions on the middleshelf, may retain a higher proportion of crystallinematerial when the liquidus path leaves the shelf. Itis unlikely that the product of partial fusion of crustalrocks would reach the upper end of the middle shelfto yield a basic magma. The general pattern en-visaged is illustrated in Fig. 2B, where D representsthe projection of a hypothetical sialic rock from themulticomponent natural system onto the plane diop-side-anorthite-albite. A process of this kind may ac-count for the dominant role of intermediate rocks inthe calc-alkaline series.

Basic-acid associations. The final liquid developed byequilibrium or moderate fractional crystallization ofbasalt is of intermediate composition. Strong frac-tional crystallization yields successively intermediateand acid liquids, and a small temperature intervalsuffices to change the liquid composition from basicto acid across the middle shelf. With the relativelyrapid cooling which might be expected in intrusionsof small or moderate size, the intermediate liquidstage is therefore unlikely to be represented by rocksof intermediate composition (cj. Nockolds, 1936). Itis, however, represented by zones in plagioclase felds-par and in ferro magnesian minerals.

Hybridization. Acid magma developed by fractionalcrystallization of basic magma persists, with littlecrystallization and little change in composition, whilethe temperature falls from the middle to the lowershelf (Fig. 4). Hybridization could occur between theacid magma and the crystalline basic rocks during theinterval of slow crystallization. Indeed, this drop fromthe middle shelf, if it exists, could be the cause of thehybridization which occurs in many basic-acid asso-ciations (e.g. Bailey et al., 1924).

Oscillatory zoning. It has proved difficult to explain

1 In other circumstances, if conditions are such that the heat ofcrystallization is lost only by conduction then the rate of crystal-lization on the shelf feature may be retarded, leading to the devel-opment of a wide range of intermediate differentiates.

DIOPSIDE-ANORTHITE-ALBITE SYSTEM 211

the oscillatory zoning exhibited by plagioclase felds-pars in terms of the steep solidus path for the systemanorthite-albite (e.g. Hills, 1936). However, the vari-ous explanations which have been proposed appearmuch more feasible if the plagioclase solidus path isgentle in the appropriate composition range. Figures1B and 3 suggest that this could be the situation formany magmas ranging in composition from basic toin termedia teo

Marginal zoning. A feldspathic basaltic magma mayprecipitate plagioclase before other crystalline phases.The solidus path for the plagioclase is then character-ized by a steep slope followed by a shelf, as illustratedin Fig. 3. This leads to the precipitation of plagioclasecrystals of fairly uniform calcic composition (soliduspath BD), or crystals of fairly uniform calcic com-position with narrow, marginal zones (BD followedby DF). Both types are present in rocks of the por-phyritic central magma type in Mull (Bailey et al.,1924, p. 241 and p. 369), and in the Stillwater com-plex (Hess, 1960, p. 41). Olivine crystals precipitatedfrom basic magmas may follow similar solidus paths.

Crystals in two generations. Many petrologists havestressed the fact that a mineral may give the appear-ance of crystallization in two generations, althoughcrystallization was perfectly continuous (e.g. Hawkes,1930). The liquidus and solidus paths illustrated inFig. 3 illustrate one of the ways in which this appear-ance could result during continuous crystallization ofa feldspathic basalt. Crystallization of the magma onthe slope AC produces a few large crystals of plagio-clase with fairly uniform composition. When theplagioclase is joined by diopside (which can be re-garded as representing the other minerals precipi-tated from the magma) crystallization on the shelfCE causes precipitation of many smaller plagioclasecrystals, in addition to the marginal zones formedaround the existing large crystals. Calcic plagioclasephenocrysts in basic rocks therefore need not repre-

REFERENCES

BAILEY, E. B. AND W. B. WRIGHT (1924) Tertiary and post-tertiary geology of Mull. Ceol. Surv. Scotland, Memo.

BOWEN, N. L. (1913) The melting phenomena of the plagioclasefeldspars. Am. Jour. Sci. Ser. 4, 35,577-599.

--- (1915) The crystallization of haplobasaltic, haplodioritic,and related magmas. Am. Jour. Sci., Ser. 4, 40,161-185.

--- (1928) The Evolution oj Igneous Rocks. Princeton Univer-sity Press.

--- AND J. F. SCHAIRER (1935) The system MgO-FeO-Si02•

Am. Jour. Sci. SeT. 5,29,151-217.HAWKES, L. (1930) On rock glass, and the solid and liquid states.

Ceol. Mag. 67, 17-24.

sent intra telluric crystallization. A similar conclusionmay be valid for olivine phenocrysts in some basicrocks.

CONCLUDING REMARKS

Phase relationships in several synthetic systemsindicate a pattern for liquidus and solidus pathswhich is characterized by changes in the slopes ofthese paths. Possibly, therefore, a similar patternapplies also in natural systems. A rather abruptchange in slope occurs on a liquidus path whenevera new crystalline phase appears in the system. Thisoccurs at the high-temperature end of the middleshelf where olivine (or more rarely, plagioclase orpyroxene) is joined by other phases, and at the high-temperature end of the lower shelf where quartz be-gins to crystallize. The changes in slope illustrated atthe low-temperature ends of the middle and uppershelves in Fig. 4 may not persist in the natural sys-tems (although changes of this kind, involving nochange in the number of phases, do exist in severalsynthetic systems) because they could be smoothedout either by fractional processes or simply by thepresence of additional components. The writer in-tends to study the melting relationships of series ofrocks in the appropriate compositional ranges inorder to test the hypothesis embodied in Fig. 4 (cf.Wyllie, 1960). If these studies confirm the suggestedliquidus profile, this introduces a "tempo" into ig-neous processes which may help to explain somepetrogenetic problems.

ACKNOWLEDGEMENTS

The writer wishes to thank H. 1. Drever, P. G.Harris, R. Johnston, W. Q. Kennedy, W. S. Mac-kenzie, P. L. Roeder and O. F. Tuttle, for kindlyreviewing drafts of the manuscript. Their sugges-tions have led to many improvements in the paper.Parts of this study are being supported by the Na-tional Science Foundation.

HESS, H. H. (1960) Stillwater igneous complex, Montana. Geol,Soc. Am. Mem. 80.

HILLS, E. S. (1936) Reverse and oscillatory zoning in plagioclasefeldspars. Ceol. Mag. 73, 49-56.

HOLMES, A. AND H. F. HARWOOD (1928) The age and composi-tion of the Whin Sill and the related dikes of the north ofEngland. Mineral. Mag. 21, 493-542.

HYTONEN, K. AND J. F. SCHAIRER (1961) Carnegie Inst. Wash-ington Year Book, 60,134-139.

NOCKOLDS, S. R. (1936) The idea of contrasted differentiation: areply. Ceol. Mag. 73, 529-535.

--- (1954) Average chemical composition of some igneous

212 PETER J. WYLLIE

rocks. Bull. Geol. Soc. Am. 65,1007-1032.RICKER,R. W. (1952) Phase equilibria in the quaternary system

CaO-MgO-FeO-Si02' Ph.D. dissertation. College of MineralIndustries, Pennsylvania State University.

SCHAIRER,J. F. (1957) Melting relations of the common rock-forming oxides. Jour. Am. Ceram, Soc. 40,215-235.

--- ANDH. S. YODER(1960) The nature of residual liquidsfrom crystallization, with data on the system nepheline-diopside-silica, Am. Jour. Sci. Bradley Vol. 258-A, 273-283.

THORNTON,C. P. ANDO. F. TUTTLE(1960) Chemistry of igneousrocks. 1. Differentiation index. Am. Jour. Sci. 258, 664-684.

TURNER,F. J. ANDJ. VERHOOGEN(1960) Igneous and MetamorphicPetrology. 2nd ed., McGraw-Hill Book Co., New York.

TUTTLE,O. F. and N. L. BOWEN(1958) Origin of granite in thelight of experimental studies in the system NaAlSiaOs-KAIShOs-

SiO,-H20. Ceol. Soc. Am. Mem. 74.WAGER,L. R. (1960a) The major element variation of the layered

series of the Skaergaard intrusion and a re-estimation of theaverage composition of the hidden layered series and of thesuccessive residual magmas. Jour. Petrol. 1,364-398.

--- (1960b) The relationship between fractionation stage ofbasalt magma and the temperature of beginning of its crystal-lization. Ceochim. Cosmochim. Acta, 20, 158-160.

WYLLIE,P. J. (1960) The system CaO-MgO-FeO-SiO" and itsbearing on the origin of ultrabasic and basic rocks. Mineral.Mag. 32, 459-470.

YODER,H. S. ANDC. E. TILLEY(1957) Carnegie Institution ofWashington Year Book, 56, 158.

---, ---, 1961. Carnegie Institution of Washington YearBook, 60, 111.

DISCUSSION

E. H. ROSEBOOM,JR. (Washington, D. C.): There are theoreticaldifficulties to predicting zoning by means of phase diagrams.There are only two types of crystallization which we can discusson a theoretical basis, perfect equilibrium crystallization and per-fect fractional crystallization. Dr. Wyllie has used the former inhis diagrams to illustrate zoning. However, by definition the crys-tals react perfectly to maintain equilibrium and thus no zoningcan occur. In perfect fractional crystallization, the bulk composi-tion by definition equals the liquid composition and the lever lawcannot be used to predict how the proportions of the crystals andliquid will change with temperature.

P. J. WYLLIE:I agree completely with Dr. Roseboom's statements,and I hope that the complete text will answer the query. Thediagrams do illustrate only perfect equilibrium conditions, andthey are used in most of the text to describe equilibrium condi-tions. It is then pointed out that with perfect fractional crystal-lization (for the original compositions used in this paper) liquidusand solidus paths follow patterns similar to those illustrated forperfect equilibrium crystallization; the changes in slope are lessabrupt. Conditions in natural environments probably lie some-where between perfect equilibrium and perfect fractional crystal-lization, and liquidus and solidus paths in natural systems maytherefore be characterized by slopes similar to those illustrated.The equilibrium diagrams can not give the range of zoning de-veloped with fractional crystallization, but in view of the fore-going remarks, they do give an indication of the differences be-tween the ranges of zoning which could be developed when (a)

paths are steep, and (b) paths cross gentle slopes. In the briefsections dealing with tentative applications to zoning in minerals,the equilibrium diagrams have been used in this qualitativefashion.

H. D. MEGAW(Cambridge, England): Does Dr. Wyllie think thatthere can be any explanation of the shape of these curves in termsof what we know of felspar structure? Anorthite has perfect sijAlalternation; this seems to be a very stable pattern. As we moveaway from the pure anorthite composition, the perfect order canstill be maintained within domains-and recent structural worksuggests that it is maintained-the substitutions being segregatedin domain boundaries, perhaps one or two cells thick. Whencompositions are too far from anorthite, this can not be main-tained without great complication. Good order is not found againtill low albite, if then. Is this apparent preference for the sijAlpattern of anorthite not likely to have a bearing on the course ofcrystallization?

P. J. WYLLIE:I am tempted to answer "yes" to such an elegantproposal. However, a similar change occurs in most systems whena crystalline phase exhibiting solid solution is joined by anothercrystalline phase. An example is provided by the system MgO-FeO-Si02, when olivine is joined by pyroxene, and here there is noordering of Si and Al to consider. Among the controlling factorsare the composition and amount of material being subtractedfrom the liquid phase. When a new phase begins to crystallize,both these factors change discontinuously, and together theycause discontinuities in liquidus and solidus paths.