Chapter 6

A Fractionation Model for Hydrous Calc-Alkaline Plutons and the Heat Budget During Fractional Crystallisation and Assimilation

Luzius MATILE, Alan Bruce THOMPSON and Peter ULMER Departementfor Erdwissenschaften, ETH Zurich, CH-B092, Switzerland

Key words: hydrous magma, thermal models, fractional crystallisation, assimilation, calc­alkaline batholith, fractionation model, hydrous and anhydrous melting

Abstract: A fractionation model has been developed for differentiation of a hydrous mantle magma. As examples of such primitive melts from successive quenched fractionates of high temperature magma batches dyke rocks cross cutting the calc-alkaline batholith of the Adamello pluton have been utilised here. The heat budget during fractionation of these magmas has been evaluated from available thermodynamic data and a generalised phase diagram. Various thermal evolution paths have been calculated in terms of assimilation behaviour of different crustal rocks. The potential for assimilation of fertile crustal rocks by later fractionates, e.g., gabbro (basalt to basaltic - andesite volcanic equivalents) is much smaller (max. 30-40% equivalent mass) compared to picrite (up to 80%).

1. INTRODUCTION

An idea of the pattern of heat evolution from magmatic plutons can be obtained from the distribution of contact metamorphic assemblages around intrusives at different depths of intrusion and at different stages in their fractionation history (e.g., see papers in Kerrick, [1992]). Some of the potentially available plutonic heat is not transported to widen the contact aureole because it is involved in melting of adjacent country rock with suitably low solidus temperatures, or the absorption of xenoliths into the magma. Stated simply, in view of the geothermal gradient, contact metamorphism will be more widespread at shallower and crustal melting at

179

N. S. Bagdassarov et al. (eds.), Physics and Chemistry of Partially Molten Rocks© Kluwer Academic Publishers 2000

180 L. MATILE et al.: Chapter 6

deeper crustal levels. Ultimately this partitioning of heat is governed by the relative rates of heat transport into the aureole compared to the rate of melting of crustal rocks and the hybridisation (melt mixing) rate. Much can be learnt from examining the time-integrated thermal processes in terms of the evolving heat budget of cooling ubiquitous calc-alkaline magma intrusions.

In this study we examine how the heat of crystallisation and the heat lost from cooling of magma and crystals is released during the successive stages of fractional crystallisation of hydrous calc-alkaline magmas. Because of their absolute dominance in batholithic suites fractionation of these magmas is much more appropriate to evaluate the role of magmas in recent crustal evolution than studies of assimilation by anhydrous basaltic or more primitive magma. We assume that the H20 in magma and in the hydrous minerals of the plutonic rocks is brought with the magma from the mantle source region. We consider that the parental magma is a hydrous picrite that arrives at the depth of "normal" continental Moho (35km -1 GPa) with a liquidus temperature of 1350°C and an initial H20-content of either 1.5 or 2.5 wt%. During the steps of fractionation the successive magma batches can separate to intrude shallower magma chambers. The present formulation permits us to examine the entire single stage fractionation history or separate steps in separate plutons. Only minor modifications to our procedure would be necessary to apply to other rarer plutonic series or to studies on anhydrous volcanics.

2. FRACTIONAL CRYSTALLISATION OF HYDROUS MANTLE MAGMA

We have developed a fractionation model [Matile, 1996] deduced from associated rock types in the calc-alkaline plutonic series of the Adamello Batholith [Ulmer, 1986]. Dyke rocks cutting the batholith are presumed to represent separate later magma batches, which have suffered only minor contamination. The chemical compositions of these dykes have been used, together with the compositions of phenocrysts that could have fractionated, to develop a liquid-line-of-descent (LLOD) for hydrous mantle magma (Table 1 and Appendix A.l).

2.1 Fractionation model

The calculated fractionation model (Appendix 1: Tables A.l and A. 2) obtained with the least-squares program PETMIX, Wright and Doherty,

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 181

[1977]) was used to relate the steps from successively fractionating magmas (dyke rocks) to the measured phenocryst minerals.

Two reference points are important to constrain in the fractionation models. The first is the composition of the unit amount of parent magma (MmO) and the second is the composition and amount of the differentiated melt before the next fractionation step (Mmi) - abbreviations are given in Table AA.

Table 1. Results of the fractionation model obtained using the program PETMIX and the rock and mineral analysis given in Appendix I. The relative masses of differentiated melts (MmiIMm") and those for the fractionated phases are all referred to the primitive picrite melt (Mm" = el in Appendix Table A,!). Mineral Abbreviations: spinel (sp), olivine (01), clinopyroxene (cpx), hornblende (hb), plagioclase (pI) and magnetite (mt).

Composition melt sp 01 cpx hb pI

picrite (el) 100 0.17 9.68

Mg-tholeiite (c2) 90.15 0.04 5.88 0.69

ol-tholeiite (c3) 83.55 3.17 1l.25

basalt (c4) 69.22 3.36 19.08 5.00

bas. Andesite (c5) 41.78 0.10 5.17 1.55

andesite (c6) 34.96 1.08 5.18 9.17

dacite (c7) 19.52

2.2 H20-contents of fractionating magmas

For a given concentration of H20 in the parental melt (here 1.5 and 2.5 wt% were chosen for illustration), the H20-contents of the successive fractionates is determined by the relative masses of hydrous phases that react during fractionation. The H20-contents so calculated are shown in the two lower panels (C and D) of Fig. 1. These concentrations lie within the ranges obtained in experiments [e.g., Ulmer, 1988] and from glass inclusions in natural mantle olivines [Sobolev and Chaussidon, 1996]. Firstly, H20-contents of fractionates without any assimilation (FC no A) were calculated for the cases of only anhydrous phases (curve 4 in Fig. ID) and for the case of hornblende crystallising (curve 5 in Fig. 1D) in the sequence shown in Table 1). By the dacite stage of fractionation the calculated H20-contents have risen to 11-13 wt% or 6 to 8 wt% for the original 2.5 or 1.5 wt% H20 in picrite, respectively. These calculated values of H20-contents of fractionated siliceous liquids (dacites) are comparable to

182 L. MATILE et at.: Chapter 6

the experimentally determined H20-contents of saturated granitoid (rhyolite) melts (horizontal lines in Fig. ID) at pressures of 1.0, 0.5 and 0.2 GPa [e.g., Shaw, 1972; Burnham and Nekvasil, 1986].

2.3 H20-contents of AFC magmas (Assimilation during Fractional Crystallisation)

The H20-content of hybrid magmas (produced when fractionating mantle magma assimilate crustal rocks) depends on the H20-content of both melts and the ratio r = (mass assimilated/mass crystallised). As an illustration (in Fig. lC), the H20-contents of evolving hybrid melts has been calculated for a constant r = 0.5, and for three different H20-contents in the assimilated crustal rocks (0, 2 and 3 wt%; curves 1, 2 and 3 in Fig. lC). A more complete discussion of the evolution of H20-concentration during an AFC process can be found by Russell et at. [1995].

While the H20-concentrations of the mantle magma (assimilant) and crustal rock (assimilate) are not known, we can usefully compare calculations of modes (Figs. 2 and 3) and H20-contents (Fig. 1 C and D) with the experimentally determined liquidus curves for various H20-contents.

2.4 Liquid-line-of-descent of fractionating magmas

As a reference liquidus curve we have used one based on that presented by Wyllie [1977] for 1 GPa pressure - 35km depth. Such an interpolated experimental curve does not necessarily reflect a true LLOD because different bulk compositions were treated as separate closed systems (both for crystal and H20-content). In addition the direct application of this curve would require the AFC magma chamber to be located at 35 km depth, so that no fractionation at deeper (nearer to source region), or shallower (emplacement depth), levels could be considered.

The liquidus curve labelled L2 in Fig. IB corresponds to suggested H20-contents [Wyllie, 1977], and the other two liquidus curves (Ll and L3) were used in some calculations to show the effects of extreme H20-contents. Also shown in Fig. IB are approximations to the H20-contents of melts of the illustrated natural rock compositions at 1 GPa [Wyllie, 1977]. Thus the liquidus curve Ll describes a fractionation path at relatively constant H20-content where constant precipitation of hydrous minerals balances assimilation of melts with very low H20-contents. The liquidus curve L3 would apply to a fractionated melt that remains H20-saturated after a basaltic composition is reached. Such a curve as L3 could only be possible at P > 1 GPa, as with increasing pressure the H20-solubility in such melts

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 183

increases. Likewise curve Ll could apply at depths corresponding to pressures less than 1 GPa.

1300

1200

1100 T

dacite andesite basalte

A :-:-: 0 % :-=::

r=------=::.., PI out --IGPa

picrite dacite andesite basalte picrite

1300

1200

[0C] 1000 - - '0.5 GPa i r@Hb out

3J$i 0l!-'5% ~at.---900

800 s% .........

_ sat.- P= 1 GPa

900

800

700 afterGREEN.1982 after WYlllE, 1977 700

15r-T-;--r-+~~~~+-~~-r-+~--~~+-~-r-T~15

10

H20

[wt%]

C AFC r=0.5 c: ~O% H20

• ... 1 .... A: 0% H20 --2-- A: 2% H20

-'3-' A: 5% H20

FC (no A) 'aI----',:--I -4 .. C: 0% H20

-5- C: ~ 0% H:P 10 ~~======--J Hp

[wt%]

5

O~~~~-L~~ __ ~~~~~-L~~~~~~~-L~ o 1.0 0.0 0.2 0.4 0.6 0.8 0.0 0.2 0.4 0.6 0.8

MJn / Mjk

Figure 1. Possible liquidus curves and H20-contents of calc-alkaline magmas fractionating from picrite, expressed as the relative mass F = MmilMmo, (A) Liquidus temperatures of plagioclase (PI) and hornblende (Hb) for basalt and andesite as a function of the H20-content of the melt (0,5 wt %, saturated) at 1.0 and 0.5 GPa [T.H. Green, 1982], (B) possible liquidus curves (Ll: constant H20-content; L3: H20-saturated fractionates) compared to an experimentally approximated LLOD (from [Wyllie, 1977]; for basalt: andesite: dacite: rhyolite, and [Ulmer, 1988] for picrite), (C) development of the H20-content of fractionates during assimilation (AFC) with r = MailMci = 0.5, and different H20-contents of the assimilate (curve 1 = 0 wt%; curve 2 = 2 wt %; curve 3 = 3 wt %). Parental magmas (picrites) with 1.5 or 2.5 wt% H20 initial content are considered, (D) evolution of the H20-content of fractionates with no assimilation (FC no A) considering only anhydrous fractionation (e.g., CIPW norm; curve 4) or with hornblende (e.g., Table 1, curve 5).

The approximate locations of hornblende and plagioclase melting reactions at 1.0 and 0.5 GPa (- 35 and 17 km, respectively) and for different

184 L. MATlLE et al.: Chapter 6

H20-contents (dry = 0; 5 wt% and saturated) are shown (Fig. lA) from the compilations by T.H. Green [1982] for basaltic and andesitic compositions.

It is thus possible to compare modes from fractionation models based upon analyses of related rocks and minerals (Table 1, Fig. 1) with those derived by reference to liquidus relations in temperature composition (T-X) sections (Fig. 1B).

2.5 Modal variation with temperatures of fractionating magma

The modal mineralogy relative to the liquidus curve L2 (Fig. lB) is shown in Fig. 2 scaled to the temperature for a pressure of 1.0 GPa (-35km). A comparison of the integrated modal mineralogy (Fig. 2A) with that normalised to the just-prior magma composition (Fig. 2B) shows that hornblende and plagioclase precipitation predominates for most of the later magmatic history. In general, stability of hornblende limits the liquidus curve to the lower crystallisation range «1l00°C), and the thermal stability of plagioclase decreases with increasing H20-content in the melt and with increasing pressure.

The form of the diagram in Fig. 2B is particularly useful because it illustrates well the modes of crystals fractionated in each step. The diagram can thus be used to evaluate whether minerals are phenocrystic or xenocryst for each calc-alkaline magmatic fractionation step.

2.6 Thermal evolution of fractionally crystallising hydrous mantle magma

Heat lost by a cooling fractionating mantle magma can be assigned to two sources; the first is the latent heat of crystallisation and the second is the heat content released on cooling related to the heat capacity (Fig. 3). We have approximated these quantities for the compositions of the fractionation stages (Fig. 3A) discussed here, using latent heat data from Richet and Bottinga [1986] and Lange and Carmichael [1990], and the temperature extrapolation method outlined by the latter workers (in Fig. 3B). To determine the integrated heat content, heat capacity data for melts and glasses were calculated following the method of Stebbins et al. [1984]; as modified by Lange and Navrotsky [1992]. These data and mineral heat capacity data from Berman and Brown [1985] were used to estimate the heat capacities of the fraction series minerals at the appropriate temperatures (Fig. 1B).

The values for latent heat of melting of the fractionates at various temperatures are shown in Fig. 3D. We have approximated the latent heat of

6. Fractionation Model for Hydrous Calc-Alkaline Plutons 185

melting for spinel and hornblende by magnetite and clinopyroxene respectively, and plagioclase was considered an ideal mixture of NaA1Si30 8

to CaAhSi20 8.

1.0 0.08

A B 0.8

~Tm= lOoe 0.06

MiJ c 0.6 illHb Min

LN~j EI PI 0.04

M:it 0.4 II Mt

0.02 0.2

0.0 0.00 900 1000 1100 1200 1300 1000 1100 1200 1300

Tm [DC] Tm [DC]

Figure 2. Modal mineralogy C£M/,jIMm") as a function of temperature for fractional crystallisation appropriate to liquidus curve L2 in Fig. I.B. (A) The cumulative modal mineralogy, £M/j of mineral j during the previous fractionation stage i is calculated relative to the composition of the parental hydrous picrite (MmO), (B) for each fractionation step i the mass crystallised M/j is calculated relative to the melt from the immediately preceeding step Mmi (LlTm = lO°C). The line MmilMmo denotes the liquid fraction during the fractional crystallisation. Mineral Abbreviations: spinel (Sp), olivine (Fo, Fa), clinopyroxene (Cpx), hornblende (Hb), plagioclase (An, Ab) and magnetite (Mt), olivine (01), plagioclase (PI).

The sharp steps in the evaluated cooling budgets in Fig. 3D reflect only the chosen calculation steps in the fractionation model. In actuality the curves would be distributed appropriate to the liquidus curves in the T-X (temperature-composition) diagram of Fig. lB.

2.7 Quantitative heat budget during fractional crystallisation

The results of combining the thermal contributions from latent heat of crystallisation and of heat content for melts and fractionated crystals is shown for two liquidus models in Fig. 4. The heat loss by the mantle magma for the temperature interval L1Tmi = (Tm O

_ Tmi) is presented as LL1Hmi

(relative to initial mass of the primary mantle melt). The panels A and B in Fig. 4 refer to the integrated heat lost for the two different liquidus

186 L. MATILE et at.: Chapter 6

configurations in the T-X diagrams of Fig. lB. The influence of the different liquidus curve is shown by the relative mass of melt (MmiIMmO). The two lower panels refer to differentiation steps of ,1Tm = lODe.

1.0

0.8

MiJ 0.6 _e_

J.:·MiJ 1 0.4

0.2

1.55

[kJ

1.45

II Sp

III Mt

~Fo

0Fa

[3 Cpx

OHb mAn BAb

500 L

[kJ/kg]

400

500

L [kJ/kg]

400

1.40 L-.............. --L_L-.............. --I_L-....... -L._L-....... --I_ .............. ___ L-.............. ---I 300 0.0 0.2 0.4 0.6 0.8 900 1000 1100 1200 1300

MInIM;:' Tm [0C]

Figure 3. Heat lost by a cooling fractionating mantle magma. The modal mineralogy (M/jIEM/i vs. MmilMm" in panel (A) has been used to partition the latent heat of melting (L. kJ/kg) of the individual minerals (panel B) and the heat capacity (em, kJ/kgK) of the summed rocks (panel C) with the help of the liquidus diagram (from Fig. l.B) to generate the latent heat of crystallisation appropriate to the three liquidus curves Ll, L2, L3 (panel D). The steps in panel D mark the individual fractionation steps of the model and have no special physical meaning. The slopes in panel D are related directly to the temperature dependence of the latent heat of individual minerals.

The heat lost by the cooling mantle magma is divided in Fig. 4 into the heat of crystallisation (MIn/US), the cooling of the melt (MImiiq), and the cooling of the crystals (MImxtai). Two cases are distinguished for the latter

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 187

(1) where all crystals fractionated down to each magma temperature (Tm i )

are included (d\ = @max = rM/IMmO), and (2) only the amount of suspended crystals taken as a constant (e.g. @x = 0.3) early in the crystallisation history. Several authors [e.g., Bergantz and Dawes, 1994] suggest two critical steps in rheological behaviour at crystal fractions of @x = 0.3 and 0.7.

Differences are seen for the two liquidus choices (Ll and L2, Fig. 4A, C and B, D) because of the implied differences in liquid/crystal mass ratio at each temperature (both have the same end-temperatures for parent and assimilate, see Fig. lB). The form of presentation of Figs. 4C and D is most useful for evaluating the heat released during each fractionation step. This is important because individual plutons usually only show a particular part of the overall fractionation history - beginning when the magma chamber permitted access of a particular fractionation product which could then parent further fractionation. With this calculated heat-loss distribution through the fractionation sequence we are now in a position to consider how this heat will be available for contact metamorphism, partial melting and assimilation - for the cases of omnipresent fractionally crystallising magmas in both continental and island arcs.

3. CRYSTALLISATION (C), FRACTIONAL CRYSTALLISATION (FC) AND ASSIMILATION (A) OF HYDROUS MANTLE MAGMAS

The heat released during magmatic fractional crystallisation is available for assimilation of adjacent rocks and for contact metamorphism. Hydrous magmas show a wider crystallisation temperature interval, and towards lower temperatures, than anhydrous magmas. This temperature difference is greater at higher pressure and would thus decrease from Moho (ca. 35 km) towards the Earths surface. For comparison with the little work available it is instructive to compare our calculated heat budgets for crystallisation of hydrous mantle magmas with those for anhydrous mantle magmas. It is easier to compare melting in anhydrous magmatic systems over a range of pressure, because the dPldT of anhydrous solidii have large positive slopes. Shown in Fig. 5A are several liquidus curves relating the melt fractions for crystallising mantle magmas as a function of temperature.

188 L. MATILE et al.: Chapter 6

IAHi m

1200 ~~A;::::;:::::;:::::;:~;:::;::::;:::;::::::;~B;::::;:::;::::;:~=;:::::;::::;:'/~ 1.0

L~ 1000

800

600

400 .... ___ ,.

200

0.8

0.6 M~

MO 0.4 m

0.2

o I-+-+-_-+---ll-I-+-~:;!--+-"'--"""+--+--+--+-~ 0.0

•...• : // D 80

......... , .......... /' ......... , .. x....... 1.2

/ ........ . ...... . .,.r---.... ".

-7 ,..... -- --- ......... . ."."" - , ~... " , .......... . - ,/ " . .::.::,...... /' ... - - _ .. .:: .... _ .. ,/ ---

0.8

60

40

20 0.2

o L..-...o.-..I-....o.--L~......L_ ........ 1-.L..._-'-_--L_--JL...-_...L-.J 0.0 900 1000 1100 1200 1300 1000 1100 1200 1300

T~ [ocl T:" [ocl

Figure 4. Heat released (1:,&lm;) from cooling fractionating mantle magma. Panels A, B: the integrated heat loss curve for the two different liquidus curves (Ll and L2 from Fig. I.B) include latent heat of crystallisation (&1,,[""), cooling of the melt (&lmli'l) , and the fractionated crystals (&ll1lxtal). Panels C, D: The heat contribution (&1m;) for the successive differentiation steps (LiT m = 1 DoC) also consider two cases of crystal accumulation; ct>x = ct>max considers all crystals to be retained; whereas ct>x = constant = 0.3 considers a fixed proportion of phenocrysts.

3.1 Crystallisation of mantle magma

As a test of the general model we compare next three liquidus curves for crystallisation of anhydrous mafic magma with the liquidus curves for the H20-bearing fractionates as used here. The curve b in Fig. 5A was used by Huppert and Sparks [1988] to consider how intrusion of dry convecting basaltic magma as sills could induce melting of continental crust. The temperature interval of crystallisation for such a basalt is narrow (70%

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 189

crystallised over 1200 e beneath the liquidus). It can be noted here that in Huppert and Sparks [1988] study the interaction of convecting mantle magma with crustal rocks induced partial melting but the melts remained separate (i.e. thermal but no chemical interaction through assimilation).

The study by Ghiorso and Kelemen [1987] modelled both equilibrium crystallisation (curve e in Fig. SA) and fractional crystallisation (curve Fe in Fig. SA) for anhydrous MORB basalt. The crystallisation interval is similar to that obtained by Huppert and Sparks for a sooe lower liquidus temperature. It is interesting that both curves are parallel because Ghiorso and Kelemen [1987] included chemical interaction (assimilation) as well as thermal interaction in their model. The curve G represents the crystallisation behaviour for an olivine tholeiite obtained by Ghiorso [1991].

The effects of H20 on the crystallisation behaviour of mantle melts obtained in this study are shown (Fig. S.A) for picrite (light lines) and basalt (heavy lines) labelled Ll, L2 and L3 (near 1 GPa). The H20-undersaturated magmas show large crystallisation intervals (70% crystallisation at 200-400 0 e below the liquidus. Thus while the overall amount of heat released will be much the same whatever the width of the crystallisation interval, the wider interval allows hydrous mantle melts to persist to much lower temperatures by displacement of the solidus - thus apparently permitting assimilation at quite low temperatures. Now we need to consider the melt fractions that will be generated with increasing temperature by anatexis of crustal rocks of different fertility.

3.2 Melt fraction increase with Temperature (T -I) for crustal rock anatexis

Fig SB shows the solidi for granitic rocks obtained experimentally [e.g.,. Wyllie, 1977] for different fixed amounts of H20 as used by Huppert and Sparks [1988]. Of the various dehydration (fluid absent) experimental studies available (e.g., see summary by Gardien et al. [199S]), the curves for pelite from Vielzeuf and Holloway [1988] and tonalite from Rutter and Wyllie [1988] have been used. The early stages of crystallisation of mantle magmas and the early stages of crustal anatexis are the most important for the present calculations of heat and mass transfer.

190 L. MATILE et at.: Chapter 6

1300 A: mantle magma B: crustal rock 1300

1200 1200

1100 1100

T 1000 1000 T [0C] rOC]

900 900

800 800

700

0.0 0.2 0.4 0.6 0.8 1.0 0.8 0.6 0.4 0.2 0.0

f Figure 5. A graph of T vs. IM/IMm" - mass crystallised relative to original mass of mantle magma. Liquidus curves (A) for mantle magma and (B) for crustal rock shown as T vs.! (melt fraction). The curves Ll, L2, L3 are the three liquidus curves from Figs. I and 3 shown as heavy lines for basalt (T m" = 1200°C) and as light lines for picrite (T m" = 1350°C). The curves FC (fractional crystallisation) and C (equilibrium crystallisation) refer to the calculations by Ghiorso and Kelemen [1987] for Mg-rich MORB, at 3kbar, H20 = 0%./02 at QFM. The curve G: anhydrous olivine tholeiite [Ghiorso, 1991]; b = anhydrous basalt [Huppert and Sparks, 1988]. Granitic country rocks from Huppert and Sparks [1988] al = 0 wt% H20, a2 = 2 wt% H20, a3 = H20-saturated eutectic; pelitic country rock (A 1 - Vielzeu! and Holloway [1988]), tonalite CA2 - Rutter and Wyllie [1988]).

3.3 The heat balance between crystallisation and assimilation

The amount of possible assimilation changes at different points in the magma differentiation sequence simply because the heat evolved by the cooling magma is not exactly linearly related to temperature from liquidus to solidus (Fig. 4). The other main effects on the degree of maximum possible assimilation of molten crustal rocks are (i) the initial temperature of the crustal rocks and (ii) their fertility to melt production (proportions of quartz: feldspar: mica that define anatectic cotectics at various pressures; [Thompson, 1996]). A lesser effect is the mechanism of assimilation -crustal rocks heated up to magma temperature or maintained at a specific solidus temperature (e.g., Bowen, [1915], p. 85). As can been seen from Fig. lB we have assumed that "granitic" melts produced by anatectic melting of crustal sources (e.g., tonalite and pelite) are identical in chemistry to those

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 191

melts resulting from fractional crystallisation of hydrous mantle magma. This means that no further eutectic is generated during assimilation and that the process of assimilation must occur via mixed melts, i.e. at a temperature above the solidus for the crustal rocks which become assimilated.

The magma masses (initial plus assimilated minus crystallised) are shown in Fig. 6 compared with the crystallised mass of mantle magma without assimilation (Ma = 0). Any assimilation will increase the magma mass and this effect is greatest in the fractionation interval from picrite to basalt (30%, Fig. 6). Subsequent mass assimilation is not great, as the ratio MmilMmo (mass of differentiated melt relative to initial parent mass) is more­or-less parallel to the Ma = 0 curve. For the assimilation mechanism of crustal rocks always heated to the magma temperature (e.g., the case of xenoliths or stoped blocks, Fig. 6A), the amount assimilated is substantially greater than for the case when the melted layer is maintained at a constant temperature (e.g., a fertile layer maintained at a segregation temperature of 900°C in Fig. 6B).

Mi m

Mfn

less fertile (tonalite)

Tg = 400°C

rg = 600°C

more fertile (pelite)

1.2 :==;::::;r=;::;::::r=;;:;:::::;;:::::::;:::::;:::::::r:::;;::::::;r::::;:;:::::r=;;;::::;;:::::;;::::::;~ 1.2

A 1.0

0.8

0.6

0.4

0.2 dacite

·"!----==-"'-.• : •• ·l.l.

TJ = Tin dacite

1.0

0.8 Min 0.6M~

0.4

0.2

0.0 L...-....... ......L._'--....L... ........ --L_""--'---L_'--....L...-""_L...-""--'-........ _.L..-..... 0.0 900 1000 1100 1200 1300 1000 1100 1200 1300

T~ T~ Figure 6. Relative masses of hybrid magmas (Mmi/Mm") as a function of magma temperature (Tm i) for crustal rocks at ambient temperatures of 400°C or 600°C, for low fertility tonalite (heavy dashed lines) and high fertility pelite (light dashed lines) relative to the melt fraction without assimilation (Ma = 0). (A) where melts from crustal rocks are assimilated at magma temperature (Ta" = Tmi; e.g. xenoliths), (B) where the partially molten crustal rocks are maintained at a constant temperature (e.g. T,/ = 900°C; e.g. a migmatite layer).

192 L. MATILE et al.: Chapter 6

3.4 Quantification of AFC-fractional crystallisation (FC) and assimilation (A)

Representative results of the thermal AFC models are presented in Table 2. The effects of shallow versus deep intrusions are easily seen for the case of country rocks with different initial temperature (TaO = 200, 600°C); the effects of magma composition are shown for picrite and basalt (TmO = 1350, 1200°C) and the effect of country rock fertility shown for tonalite and more fertile pelite (second values in brackets). The relative assimilated or crystallised masses are shown by IM/IMmo vs. IMailMmo, and r = MailMci values for the beginning (r, TmO) and end of fractionation (r, Tmi ). The results include fractionation until an andesitic composition is reached (Tmi

=1000°C).

Table 2. Results of thermal AFC modelling for assimilation of crustal rocks at shallow and deeper levels (Ta" = 200, 600°C) by pi critic or basaltic magma (Tm" =1350, 1200°C). The results for assimilation of more fertile rocks are given in parentheses (pelite compared to tonalite). Results are given up to an andesitic fractionated magma composition (Tmi = 1000°C) as totally assimilated and crystallised relative masses (EM/IMm", EMaiIMm") and as the ratio of assimilated and crystallised masses (r = M,/IM,i) at the beginning and end of the AFC process.

Too rOC] Tm roC] EM,/IMm" EM/IMm" r (Tm") r (Tmi)

200 1350 0.49 (0.60) 0.85 (0.88) 0.96 (0.94) 0.26 (0.46) 200 1200 0.25 (0.37) 0.60 (0.63) 0.88 (0.89) 0.26 (0.46) 600 1350 0.83 (1.07) 0.98 (1.04) 1.29 (1.33) 0.48 (0.81) 600 1200 0.44 (0.66) 0.66 (0.71) 1.29 (1.33) 0.48 (0.81)

The results of the calculations in the present study are most usefully presented as IM/IMmo vs. IM,/IMmo diagrams (e.g., Fig. 8). The relative amount of hybrid melt F = 1 - IM/IMmo + IMailMmo can be related to the amount crystallised at any step and to the amount assimilated. The zero assimilation case (Ma = 0) is equivalent to perfect fractional crystallisation. The ratio r = MailMci relates the mass assimilated to the mass crystallised. On the integrated scales (Fig. 7 A) the diagrams can be read as fractionation paths. Thermal petrological quantification of the FC sequences discussed above (i.e. heat balance following a mass-balance for fractionation) when combined with assimilation of country rocks of different fertility and initial temperature leads to an evaluation of APC paths that can be compared to modal mineralogy and geochemical signatures within plutons.

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 193

3.5 AFC processes for FC of hydrous picrite and assimilation of tonalite

As an example of an APC path for fractionating mantle magma interacting with crustal rocks, we illustrate in Fig. 7 A the case of a fractionating hydrous picrite (Tliquidus = 1350°C at 1.0 GPa) interacting with tonalite (initially at 400°C). Here the mass balance of Table 1 (see also Appendix Table A. 1) and Fig. 2 are combined with the alternative liquidus curves Ll, L2 and L3 (Fig. 2B), the cooling thermal histories of Fig. 4A, B and the melting curves for crustal rocks (Fig. 5), to derive the APC paths.

- -LI- _.

-12-

·····13······

cl: picrite c2: Mg-tholeiite c3: OI-tholeiite c4: basalte

c5: bas. andesite c6: andesite

c7: dacite

1.5 r--,....-.... --...,..----r~__,-.......,r_-T""_-..,._-""T"""...,........, 1.5

1.0

0.5

A tonalite

rg=400cC

900

./ 1.0

0.5

J-o--~~L-....... ...L.~--L_-l' Ij _____ --L_---JL...-_.L-_....I 0.0

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 1.0

Figure 7. AFC model (LA{iIMmO vs. IM,/IMmO) for hydrous picrite (liquidus at 1350DC at 1.0 GPa) assimilating tonalite initially at (A) 400DC and (B) 600DC. The fractionated rock sequence (Table I, Appendix Table A. I) are related to the AFC parameters via the liquidus diagram (L2 in Fig. IB). The liquidus temperatures (T, DC) appropriate to the fractionated liquid compositions (c2 to c7) are indicated for the liquidus curves Ll (left) and L3 (right). The F values refer to the relative magma mass (F = MmilMmO) and the r values to the mass ratio assimilation/crystallisation. The superimposed Fir contours permit comparison with geochemical models of assimilation [e.g., Aitcheson and Forest, 1994].

194 L. MATlLE et al.: Chapter 6

For the case of assimilation of tonalitic crustal rocks initially at 400oe, the successive paths from picrite (c 1) to Mg-tholeiite (c2) to olivine-tholeiite (c3) to basalt (c4), practically follow the contours F = 1; r = I (Fig. 8B). For these fractionation stages the amount of assimilation (- 40%) almost equals (r = 1) the amount of crystallisation for the hybrid magma, because in this example the magma mass remains almost constant. The fractionation step from basalt (c4) to basaltic andesite (c5) results in further 20% assimilation of 4000 e tonalite together with 20% crystallisation. The final step from andesite (c6) to dacite (c7) results in a further - 7% assimilation with a further 40% crystallisation.

It is important for future studies to confirm whether the liquid lines of descent for AFC of hydrous mantle magmas lies outside the envelope indicated for Ll, L2 and L3. The present considerations appear to suggest that a more detailed knowledge of the LLOD will not modify the AFC history as much as the variation of the other two main factors, (i) country rock initial temperature, and (ii) country rock fertility. The effect of the former effect - increased country rock temperature is shown in Fig 7 B.

The higher country rock initial temperature at 600°C (Fig. 7B) results in considerably more assimilation of tonalite by fractionating hydrous picrite than 4000 e as discussed above. The higher degree of assimilation results in F and r> 1.0 in the first steps (c 1 to c4) and a higher ratio of assimilation to crystallisat~on throughout the history compared to assimilation of 400°C tonalite.

3.6 A comparison of the efficiency of AFC processes for picrite assimilating different crustal rocks at different temperatures

The effect of initial country rock temperature on the AFe path discussed with regard to Fig. 7 at 400°C and 600°C, is shown also at 2000 e and 8000 e in Fig. 8A. Because temperature of 2000 e corresponds to the ambient temperature at a depth of 10 km for a geothermal gradient of 20°C km'!, this represents a lower bound to the whole processes of contact metamorphism around plutons. A temperature of 8000 e represents the case where mid­crustal rocks have been heated close to or above their solidus. To achieve ambient temperatures near 800°C requires heat transfer processes that need to have resulted from a hot geotherm. These include massive intrusion of previous mantle magma batches, or upwelled asthenosphere responding to extensional thinning of overlying lithosphere or delaminative removal of dense eclogitic rocks in thickened lower crust.

The paths in Fig. 8A show the AFC evolution of the hydrous picrite parent towards lower temperatures during assimilation of crustal rocks at

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 195

different ambient temperatures. These in tum can be related to characteristic depths for specific steady-state geothermal gradients. The partitioning between A and FC during the successive fractionation steps can be seen well in Fig. 8B. The line segments here connect points and should not be thought of as paths, but rather as showing the degrees of A vs. FC compared to the previous step. With this simplified concept it can be seen that the initial country rock temperatures separate out regions where degree of crystallisation is continually decreasing up to near 600°C from a region where both A and FC continue to increase (above 600°C).

3.7 The effect of rock fertility upon AFC histories

As an example of rocks more and less fertile to crustal anatexis we have chosen a pelite and a tonalite. Both these rock types contain hydrous minerals which undergo dehydration melting. Thus the concept of fertility to anatexis embodies the notion that the H20 required to generate melt at the much lower temperatures compared to anhydrous conditions is locally available in particular minerals but in restricted amount. Other approaches [e.g., Huppert and Sparks, 1988] consider a fertile rock composition (the appropriate modal combinations of quartz and feldspars to generate "granite minimum" melts) with fixed amounts of externally added H20 (our Fig. 5B). This adds the complication to the geological processes under consideration of needing also to explain, the migration of H20 through a "hygroscopic" environment that will efficiently remove circulating fluid by melting or generation of hydrous minerals.

Vielzeuj and Holloway [1988] have investigated the melt fraction if) with increasing temperatures (T) for the dehydration melting of pelite, as have Rutter and Wyllie [1988] for tonalite. These two studies bracket available studies of determination of f vs. T for a whole range of crustal rocks (as summarised by Gardien et al. [1995]).

As can be seen the effect of these quite different fertilities on the melt fraction if, from Fig. 5B) is largest up to 900°C and steadily diminishes towards 1150°C (Fig. 8A) - it is roughly equivalent to a 200°C difference in initial country rock temperature. This observation is potentially useful in field studies where the chemical effect of degree of assimilation due to type of country can be distinguished from thermal effects due to difference between magma and country rock temperatures at different depth of intrusion.

196

TO [0C] 200

1.0

0.8

LMj 0.6

MO m 0.4

0.2

1.5

C r:: =4000C

1.0

LMj MO m

0.5

0.0

0.0 0.2 0.4

L. MATILE et al.: Chapter 6

400

0.6 0.8 0.0

I:Mi/MO a m

tonalite 600 800

pelite

~ 10 ... ,-., ~ \:>.

.... ~ " " .... ~

/ I

t1T m= IOoe

D r:: = 600"C

## "" 12000C ._ .... _---.,_ ... _--_ .. _-----------_ .... _----------------_ ....

""'~300OC , 0.2 0.4 0.6 0.8 1.0

(JJ:Mj./ Min)

0.10

0.08

0.06 Mi ..::=

0.04 Mi m

0.02

1.5

1.0

LM~ MO

m

0.5

0.0

Figure 8. APC plots (lliciIMm" vs. lliailMmO) illustrating (A) the effect of country rock initial temperature (TaO) and fertility (Fig. 58) on the complete AFC path for fractionating hydrous picrite, (B) the successive fractionation steps from hydrous picrite to Mg-tholeiite (l300°C), olivine tholeiite (l200°C), basalt (I 100°C), andesite (lOOO°C) to dacite (900°C),. (C) a comparison of the effect of fertility of country rock (Fig. 58) upon the AFC paths for assimilation by liquids that previously underwent fractionation from parent to daughter with no assimilation. Considered for ambient country rocks initially at 400°C (20km for a steady state gradient of 20°C km·\ (D) as C but for To = 600°C.

6. Fractionation Model/or Hydrous Calc-Alkaline Plutons 197

3.8 A comparison of AFC paths for hydrous basalt magmas compared to picrite

In fractionating from 1150°C to 900°C basalt can assimilate up to 40% pelite compared to 20% tonalite (Fig. 8C). The picrite fractionation from 1350°C to 900°C could assimilate 90% pelite and 70% tonalite (Fig. 8A). Assimilation is much more efficient if the process starts at the beginning of the differentiation of primary mantle magmas because of two reasons: (1) the r-values are highest in the beginning of differentiation, and (2) because an early increase in the mass of the assimilating magma will result in a later release of heat from crystallising and cooling of the hybrid compared to the non-contaminated magma - otherwise the heat will be lost to contact metamorphism.

3.9 Assimilation by fractionating melts adjacent to magma chambers at successively higher crustal levels

A simple but plausible scenario is that successive magma fractionates escape to successively shallower magma chambers where they can undergo wall rock reactions with rocks at progressively lower initial ambient temperatures. We have shown in Fig. 8C, D the case where fractionation without any assimilation generates the successive fractionates as labelled and these begin assimilation at later stages as indicated. Both pelite and tonalite are considered initially at 400°C (Fig. 8C) and 200°C (Fig. 8D). Assimilation in shallow magma chambers (between 20 and 10 km) is evidently quite restricted « 10%).

3.10 Effects of other variables on the AFC paths

The crystal fraction (tPx ) in the mantle magma could affect the heat balance in two different ways :(1) the additional heat capacity term Mfmxtal

(Fig. 4) could increase the amount of assimilation by <10% if the crystal fraction is very high (Matile [1996], p.89). Primitive magmas with a high potential for assimilation are generally crystal poor, and intermediate magmas with more crystals have a low potential for assimilation. (2) Reaction of fractionated crystals with the melt could lead to a decrease in assimilation.

Assimilation of crustal rocks in mantle magmas requires both their melting and the mixing of the crustal melt with the mantle magma. Incomplete mixing, depending on magma dynamics and diffusion rates, could therefore lower the amount of assimilation.

198 L. MATILE et al.: Chapter 6

The chemical effect of assimilation of typical crustal rocks on the amount of subsequent crystallisation in the magma was found to be of minor importance for the heat balance «5%, Matile [1996], p. 54).

4. COMPARISON OF THE HEAT BALANCE FOR AFC PROCESSES WITH OTHER RESULTS FOR CRUSTAL MELTING

By considering crustal rocks at different pre-intrusion temperatures it is possible to model intrusions into any particular crustal depth by reference to ambient continental geotherms. Intrusion during orogenesis can also be modelled with the present integrated techniques because orogenic timescales are usually at least an order of magnitude greater than pluton cooling timescales. Thus contact metamorphism is implicitly included in these models even though we have not displayed the heat transfer outside the magmatic system.

Our study is distinct in that we consider hydrous fractionating magmas that assimilate crustal rock types which supply the H20 for their melting by dehydration melting of paragenetic hydrous minerals. Parts of our modelling can be compared with two other studies that evaluate the heat evolved from cooling mantle magmas by examining the degree of assimilation of particular crustal rocks.

4.1 Crustal melting following basaltic underplating

Partial melting of overlying crust by underplated basaltic magma has been considered by several authors [e.g., Huppert and Sparks, 1988; Bergantz, 1989]. The results of Huppert and Sparks [1988] calculations have been reformulated in terms of our APC model in Table 3 and Fig. 9. They considered a 500 m thick basaltic sill which induced melting in a overlying layer of crustal rocks (Tm O = 1200°C and Tm60% = 1091°C (temperature at the time of 60% crystallisation), with T-f curves for mantle magma (Fig. SA). We are not concerned here with the mode of heat transfer as we deal only with time-integrated heat available.

The crustal rocks considered had different H20-contents and T-f curves as in Fig. 5B and different initial temperatures (Table 3 here). Following their Table 4 the results in our Table 3 were obtained - which indicates that after a time t (years), a sheet of granite melt is formed with thickness a (m), temperature Tat (0C) and a melt fraction, f. These values permit us to evaluate the mass of granite melt relative to the mantle magma M,/IMmo

(open circles in Fig. 9). The second calculated mass fraction M/IMmo

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 199

(closed circles in Fig. 9) is higher because the conductive heat flux was not considered. These values are plotted in Fig. 9 using the calculated values of LM/IMmo versus LMajMmO with contours of the approximate temperature (Tmi, DC).

Table 3. The results of Huppert and Sparks [1988] (Table 4) recalculated in terms of the present AFC models, for the case of a 500m thick basalt sill with Tmo = 1200°C and Tm60% = 1090°C for the time at 60% crystallisation. The assimilated crustal rocks have granite to granodiorite composition with different H20-contents referred to the melting diagram in Fig. 5. After a time t (years), a sheet of granitic melt of thickness a (m), temperature To' (0C) and a melt fraction if) can form. From the methods outlined here the mass of granitic melt relative to mantle magma can be evaluated for the case including conductive heat flow (M/IMm" or excluding the conductive heat flow (M,/IMmO).

Country rock T,/' rOC] t [y] a [m] To' [0C] f M/IMmo M,/IMmo

al) H20 = 0% 500 658 197 1010 0.57 0.19 0.29 a2) H20 = 2% 500 89 295 934 0.66 0.33 0.36 a3) eutectic 500 76 276 910 1.00 0.47 0.51 a2) H20 = 2% 750 90 498 939 0.68 0.58 0.64 a2) HP=2% 850 91 688 943 0.70 0.82 0.91

The models here for comparison (Fig. 9) are calculated in the following ways continuing the development for Figs. 7 and 8. Examples are shown for country rock temperatures (pelite or tonalite) between 400 and 600De in Fig. 9, and starting magma compositions of olivine-tholeiite and basalt.

Not only is the correspondence between the different calculations reassuring it also indicates that the heat contribution of mixing must certainly be small compared to the other exothermic and endothermic contributions, and that our assumptions concerning the role of H20 in magma fractionation are adequate.

4.2 Anhydrous MORB assimilating albite and pelites

The assimilation calculations of Ghiorso and Kelemen [1987] who considered anhydrous Mg-rich MORB as the mantle magma at a depth 10 km (0.3 GPa, withfo2 buffered by QFM). They set the magma temperatures as 12S0De for this anhydrous system and considered assimilation of albite and two pelitic compositions. Their results are shown in Table 4 for heat balance-assimilation calculations for crust samples originally at 12S0De and sooDe together with the factors derived from the procedures developed in this study. The results for the sooDe calculations are plotted in Fig. 9 using the calculated values of MalMm" and MJMmo.

200 L. MATILE et al.: Chapter 6

Table 4. The results of Ghiorso and Kelemen [1987] recalculated in terms of the present AFC models for an Mg-rich MORB (TmO =1250°C) at 3kbar with /02 at the QFM buffer. For assimilation of pelite (Qz-Ilm-Ksp-Opx-Spn-Plg), pelite B (Qtz-Ilm-Mus-Bio-Gar-Plag) or albite the magma temperatures are given as Tmi [0C], at two country rock temperatures (Ta" = 1250, 500°C) for the case of complete melting if = I). The results are given in terms of relative assimilated mass (M,JMmO), relative crystallised mass (McIMmO), ratio of assimilation to crystallisation (r = Mu IMJ, and relative mass of mantle magma (F = MmiIMmO). Some results for fractional crystallisation (Fe) versus equilibrium crystallisation (EC) are given for comparison).

assimilate Tao [0C] Tm i [0C] M/Mm" M/Mmo r=M/Mc F= MmilMm"

- (FC) 1190 0.00 0.77 0.00 0.21 - (EC) 1190 0.00 0.64 0.00 0.35 albite 1250 1212 0.40 0.00 1.40 albite 500 1190 0.28 0.67 0.40 0.60 pelite A 1250 1215 0.40 0.08 4.86 1.32 pelite A 500 1190 0.34 0.91 0.44 0.77 2elite B 500 1190 0.22 0.63 0.64 0.63

1.0 r--""T'"--.-....---r...,..~..."..........,..---r-_--. ~-----------,

J:Mi __ c

M/i,

9000 e

• I~' ,. ,

J .' I~' .. ; ,/ , / " , ,

tJ---I-/7~ / I / 'l000oe -, I ' I, .. ~.,'

.'~i f./ /'

0.8 FC

EC /1. f, , 0.6 ~----<~i .... ce.~-,Ai. a=-,~,L---1100°C

1000oe' ,. /,.' " .. i ," , , ./ '/' " i .' ~ I~ " .. Il' ll' ,

.' l'~ llOOOe I • 'I, I I ,

.1;1",'

0.4

..' ~ I;,;, 0.2 /'i.~l :' llOOoe q-;J' ##

i'~" ~11000e

tonalite 4000 e 6000 e

petite

tonalite 4000e 6000 e

petite

0- Huppert & Sparks, 1988 • Ghiorso & Kelemen, 1987

0.0 L..._ ........ '--_--I. __ -'-_~_'_ _ ____I L-_________ --I

0.0 0.2 0.4 0.6 0.8 1.0

Figure 9. Comparison of the present AFC models (W/IMmo vs. WailMmO) and the crustal melting models without assimilation (FC-A) with the results from other studies. Calculations were made for country rock temperatures Tuo = 400 and 600°C and for different country rock fertilities (pelite, tonalite, Fig. 5B). The results of Huppert and Sparks [1988] consider extensive melting of a granitic layer by an adjacent basaltic intrusion but without magma mixing. Table 3 shows the results for a calculated 60% crystallisation of basalt - open circles for M/IMmo include conductive heat flow, closed circles for M}IMm" are independent of heat flow. The result for AFC modelling from Ghiorso and Kelemen [1987] (see Table 4 here) are shown by solid squares.

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 201

At shallower depth (lower pressure, e.g. 0.3 GPa as used by Ghiorso and Kelemen [1987]) the fractional crystallisation interval between liquidus and H20-saturated solidus is significantly less than at 1 GPa - because of the negative dPldT of the H20-saturated solidus reflecting increased H20-solubility with increased pressure.

The expansion of the partially melted region to lower temperatures is the major effect of adding H20. The thermal terms associated with mixing or crystallisation of hydrous minerals is much smaller than for latent heat and heat content.

S. CONCLUSIONS

For hydrous mantle magmas fractionating from parental picrite at 1 GPa (- 35km), the largest amount of heat evolution occurs during the beginning of fractionation of Cpx joining olivine. This step corresponds to the pre­basaltic stage from Mg-tholeiite to olivine-tholeiite (i.e. around 1250°C to 1200°C in the present example, Figures 4 and 5). These fractionates will be rare in plutonic complexes (as are those of the parental picrites) because such liquids will be routinely modified by contamination resulting from assimilation. Pi critic magmas are reported as primary melts from some active volcanic centers (e.g. 1967 Halemaumau and Hiiaka eruptions on Hawaii [Nicholls and Stout, 1988]).

The occurrence of dyke rocks cutting the Adamello pluton has been utilised here as an example of such primitive melts from a subsequent high temperature magma batch. The potential for assimilation of fertile crustal rocks by later fractionates, e.g. gabbro (basalt to basaltic andesite volcanic equivalents) is much smaller (max. 30-40% equivalent mass) compared to picrite (up to 80%). The ability to identify mantle signatures in basalts and gabbros is itself an indication of lesser degree of contamination.

Crustal rocks already heated close to their solidus (- 800°C, Fig. 5) will be the most efficient assimilates. For rocks at ambient temperatures of between 400 to 600°C, equivalent amount of assimilation and crystallisation will result. For ambient rocks at 200°C assimilation is much less efficient. The most efficient assimilation will be in the high temperature melts (picrite to basalt in our study).

The style and extent of assimilation will be much more extensive for magma chambers ponded within the crust, compared to rapidly ascending magmas reacting with conduit walls, or by thermal erosion of underlying crust by flowing lavas after eruption.

To preheat the crustal material to its solidus requires the total heat from early small batches of magma which lose heat so fast that they can only

202 L. MATlLE et at.: Chapter 6

assimilate very little. Only large bodies (10 km size) of fractionating hydrous mantle magma can assimilate efficiently

This work provides background for further studies directed at determining the rates of heat transfer within and from the commonest type of magmatic intrusions, as well as on the diffusion rates of hybridising magmatic components during mixing. It is possible to extrapolate the fractionation steps obtained here to lower pressures appropriate to emplacement depths of magmatic intrusions at various depths within continental crust. Such studies are necessary to understand the controls on the depth of emplacement of magma chambers.

ACKNOWLEDGMENTS

We thank George W. Bergantz for commenting on the paper and Didier Laporte for acting as editor. This work was supported by an ETH research credit no. 0-20-711-93.

APPENDIX 1. FRACTIONATION MODEL FOR CALC· ALKALINE MAGMAS

The calculation of the fractionation model follows stepwise a melt composition to the next level by considering phenocryst phases of measured composition. Assimilation is included into these fractionation models based upon the assumption that the liquid-line-of-descent will not be influenced by small degrees of assimilation ( see Ghiorso and Kelemen [1987] for a discussion of when and when not the LLOD will be effected). Thus the composition of the assimilating magmas (c1-c7) and the composition of the crustal melts (assimilates: a2, a7, a9, all) are listed together with the measured compositions of phenocryst phases in Table A.l (from Ulmer [1986]; and unpublished data).

The calculated fractionation model (Appendix Table A.2) obtained with the least-squares program PETMIX [Wright and Doherty, 1977] was used to relate the steps from successively fractionating magmas (dyke rocks) to the measured phenocryst minerals (Table A.I).

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 203

Table A.i. Rock and mineral analyses used with fractional crystallisation (FC) and assimilation - FC modelling. The composition (wt %) of the calc-alkaline dyke rocks (el -c7) and of their phenocrysts (sp, 01, cpx, hb, pi, mt, grouped by the sample numbers) are the basis of the fractionation model - new mineral analyses below, bulk rocks from Ulmer [1986]. The composition of the assimilates used for the calculations are a2 (pelite: Vielzeuf and Holloway [1988]), a7 (amphibolite: Beard and Lofgren [1991]), a9 (biotite granite: Wyllie [1977]) and all (biotite gneiss: Patino Douce and Beard [1995]).

Si02 Ti02 AI20 3

FeO MnO MgO CaO Na20 K 20 Cr20S NiO Total

Si02 Ti02

AI20 3

FeO MnO MgO CaO Na20 K 20 Cr20S NiO Total

Si02 Ti02

AI20 3

FeO MnO MgO CaO Na20 K 20 Cr20S NiO Total

cl

47.54 0.73 13.31 9.42 0.17 16.43 10.33 1.25 0.45 0.15 0.05 99.63 a9

75.40 0.15 13.50 0.64 0.04 0.10 1.00 4.00 4.60 0.00 0.00 99.43

CPX3

51.72 0.37 3.98 4.49 0.08 15.72 22.88 0.21 0.00 0.53 0.01 99.99

c2

48.85 0.67 15.01 8.69 0.17 13.00 11.38 1.80 0.57 0.08 0.02 100.1 all

72.70 0.45 14.90 1.70 0.11 0.54 1.63 2.16 5.76 0.00 0.00 99.95 CPX4

51.19 0.42 3.70 5.48 0.12 16.16 22.30 0.24 0.00 0.40 0.00 100.0

c3

50.20 0.69 15.86 8.43 0.16 10.31 11.83 2.16 0.59 0.06 0.01 100.3 01]

41.01 0.01 0.02 8.61 0.14 49.67 0.14 0.00 0.00 0.00 0.29 99.89 hb4

42.91 2.23 13.12 12.22 0.18 14.86 11.78 2.37 0.29 0.03 0.00 99.99

c4

51.39 0.70 17.93 8.34 0.12 7.23 10.52 2.54 0.58 0.04 0.01 99.40 012

39.82 0.00 0.01 10.97 0.39 48.44 0.19 0.00 0.00 0.02 0.14 100.0 hbs 42.41 1.65 14.48 11.06 0.15 14.89 12.48 2.42 0.43 0.03 0.00 100.0

c5

55.47 0.72 19.06 7.08 0.13 3.81 8.82 3.08 1.25 0.01 0.00 99.43 013

39.82 0.00 0.01 10.97 0.39 48.44 0.19 0.00 0.00 0.02 0.14 99.98 hb6

46.40 0.85 9.38 16.86 0.66 11.65 12.22 1.07 0.92 0.00 0.00 100.0

c6

59.34 0.56 18.92 6.51 0.10 2.38 8.06 2.77 0.84 0.01 0.00 99.49 sp]

0.26 0.40 13.03 26.43 0.42 11.96 0.03 0.01 0.02 47.26 0.19 100.0 pl4

46.18 0.04 33.77 0.76 0.01 0.15 17.51 1.45 0.12 0.00 0.01 100.0

c7

69.97 0.34 15.94 2.67 0.10 1.10 4.04 3.15 2.40 0.00 0.00 99.71

SP2

0.26 0.40 13.03 26.43 0.42 11.96 0.03 0.01 0.02 47.26 0.19 100.0 pis

45.72 om 34.31 0.45 0.01 0.01 18.27 1.20 0.02 0.00 0.01 100.0

a2

69.30 0.60 17.20 2.40 0.00 1.60 1.70 3.50 3.70 0.00 0.00 100.0

SP3

0.00 0.37 11.75 26.03 0.60 10.93 0.02 0.00 0.00 50.24 0.07 100.0 pl 6

49.35 0.03 32.20 0.18 0.01 0.05 15.34 2.74 0.1 I 0.00 0.00 100.0

a7

72.31 0.59 15.30 2.93 0.06 0.87 3.76 3.05 0.96 0.00 0.00 99.83 CPX2

51.66 0.39 3.87 4.73 0.10 15.80 22.82 0.21 0.00 0.42 0.00 100.0 mtS,6 0.00 3.92 0.83 94.53 0.62 0.00 0.04 0.00 0.01 0.02 0.03 100.0

204 L. MATILE et at.: Chapter. 6

Table A.2. The calculated fractionation model obtained with the least-squares program PEfMIX [Wright and Doherty, 1977] was used to relate the steps from successively fractionating magmas (dyke rocks) to the measured phenocryst minerals (Table A.I).

MailMm"i 01] Sp] M/IMmai M/iMmi M/IM/ c1 ~c2 0.00 0.0968 0.0017 0.1016 0.1020 1.000 (c1+a2) ~ c2 0.01 0.0966 0.0017 0.1035 0.105 1.029

0.02 0.0923 0.0017 0.1030 0.105 1.034 0.05 0.0872 0.0015 0.1091 0.115 1.130

(cl+a7) ~ c2 0.01 0.0947 0.0017 0.1028 0.104 1.022 0.02 0.0927 0.0017 0.1043 0.106 1.048 0.05 0.0865 0.0015 0.1088 0.115 1.127

(c1+a9) ~ c2 0.01 0.0945 0.0017 0.1023 0.103 1.017 0.02 0.0924 0.0017 0.1042 0.106 1.047 0.05 0.0871 0.0015 0.1122 0.118 1.162

(c1+all) ~ c2 0.01 0.0943 0.0017 0.1017 0.103 1.011 0.02 0.0918 0.0017 0.1023 0.104 1.027 0.05 0.0863 0.0015 0.1093 0.115 1.132

M,/IMmai 013 CpX3 Sp3 McilMmai M/iMmi M/IM/ c3 ~c4 0.00 0.0379 0.1346 -0.0009 0.1732 0.173 1.000 (c3+a2) ~ c4 0.01 0.0375 0.1290 -0.0008 0.1678 0.169 0.979

0.02 0.0373 0.1230 -0.0008 0.1619 0.165 0.954 0.05 0.0363 0.1050 -0.0006 0.1447 0.152 0.879

(c3+a7) ~ c4 0.01 0.0373 0.1304 -0.0009 0.1688 0.171 0.984 0.02 0.0365 0.1259 -0.0008 0.1639 0.167 0.966 0.05 0.0345 0.1130 -0.0007 0.1507 0.159 0.916

(c3+a9) ~c4 0.01 0.0375 0.1289 -0.0008 0.1677 0.169 0.978 0.02 0.0370 0.1235 -0.0008 0.1627 0.166 0.959 0.05 0.0354 0.1072 -0.0006 0.1476 0.155 0.897

(c3+all) ~c4 0.01 0.0373 0.1296 -0.0009 0.1685 0.170 0.983 0.02 0.0368 0.1247 -0.0008 0.1639 0.167 0.966 0.05 0.0355 0.1092 -0.0006 0.1500 0.158 0.912

MailMmai CpX4 Hb4 PI4 M/IMmai McilMmi M/IM/ c4~c5 0.00 0.0446 0.2756 0.0723 0.3974 0.397 1.000 (c4+a2) ~ c5 0.01 0.0478 0.2680 0.0654 0.3816 0.385 0.970

0.02 0.0467 0.2615 0.0585 0.3668 0.374 0.942 0.05 0.0445 0.2401 0.0386 0.3224 0.339 0.854 0.10 0.0401 0.2061 0.0061 0.2494 0.277 0.697

(c4+a7) ~ c5 0.01 0.0487 0.2678 0.0663 0.3833 0.387 0.974 0.02 0.0487 0.2591 0.0606 0.3690 0.377 0.947 0.05 0.0493 0.2347 0.0434 0.3270 0.344 0.866 0.10 0.0500 0.1945 0.0154 0.2583 0.287 0.722

(c4+a9) ~ c5 0.01 0.0485 0.2655 0.0632 0.3776 0.381 0.960 0.02 0.0485 0.2555 0.0543 0.3583 0.366 0.920 0.05 0.0484 0.2253 0.0284 0.3008 0.317 0.797 0.10 0.0479 0.1780 -0.0130 0.2091 0.232 0.585

6. Fractionation Modelfor Hydrous Calc-Alkaline Plutons 205

MailMmai CpX4 Hb4 PI4 M/IMmai M/IMmi M/IM/ c4 -+ c5 0.00 0.0446 0.2756 0.0723 0.3974 0.397 1.000 (c4+all) -+ c5 0.01 0.0485 0.2660 0.0645 0.3795 0.383 0.965

0.02 0.0484 0.2576 0.0568 0.3631 0.371 0.932 0.05 0.0484 0.2310 0.0353 0.3146 0.331 0.833 0.10 0.0476 0.1884 0.0007 0.2364 0.263 0.661

M(/IMm(Ji PI6 Hb6 MtS.6 McilMmai McilMmi M/IM/ c6 -+ c7 0.00 0.2623 0.1483 0.0308 0.4371 0.437 1.000 (c6+a2) -+ c7 0.01 0.2581 0.1469 0.0305 0.4310 0.435 0.996

0.02 0.2536 0.1454 0.0302 0.4245 0.433 0.991 0.05 0.2405 0.1418 0.0289 0.4062 0.428 0.978 0.10 0.2196 0.1353 0.0256 0.3762 0.418 0.956

(c6+a7) -+ c7 0.01 0.2598 0.1463 0.0306 0.4368 0.441 1.010 0.02 0.2565 0.1450 0.0304 0.4317 0.440 1.008 0.05 0.2485 0.1395 0.0299 0.4179 0.440 1.006 0.10 0.2339 0.1314 0.0288 0.3941 0.438 1.002

(c6+a9) -+ c7 0.01 0.2572 0.1459 0.0304 0.4290 0.433 0.991 0.02 0.2528 0.1427 0.0301 0.4208 0.429 0.982 0.05 0.2381 0.1355 0.0289 0.3976 0.419 0.958 0.10 0.2154 0.1219 0.0256 0.3590 0.399 0.913

(c6+all) -+ c7 0.01 0.2581 0.1460 0.0305 0.4301 0.434 0.994 0.02 0.2534 0.1437 0.0302 0.4226 0.431 0.987 0.05 0.2404 0.1376 0.0292 0.4026 0.424 0.970 0.10 0.2198 0.1271 0.0278 0.3706 0.412 0.942

APPENDIX 2. LATENT HEAT OF CRYSTALLISATION

Table A.3. Experimental values of latent heat of crystallisation (kJ/mo!) for magmatic minerals at the melting temperature (Tf • K). The values for the glass transition temperature (Tg• K) are taken from Richet and Bottinga [1986]. If not known then it is assumed that Tg = 1100K.

Mineral L (Tt) [kJ/mol] Tf [K] Tg [K] reference

Si02 (Q) 94.0 ± 1.0 1700 1607 Richet et al. [1982] KAISi30 R (Or) 54.0 ±4.0 1500 1178 Richet and Bottinga [1984a] NaA1SiPR (Ab) 64.3 ± 3.0 1373 1018 Richet and Bottinga [1984a] CaAI2Si20 R (An) 133.0 ±4.0 1830 1085 Richet and Bottinga [1984b] AI20 3 (C) 107.5 ± 5.4 1870 Barkhatov et al. [1973] FeTi03 (11m) 21.7±0.1 1640 Naylor and Cook [1946] Fe304 (Mt) 138.1 1870 Robie et al. [1978] CaMgSi20 6 (Cpx) 137.7 ± 2.4 1665 1026 Lange et al. [1990] MgSi03 (Opx) 73.2 ± 6.0 1834 1026 Richet and Bottinga [1986] Mg2Si04 (Fo) 114 ± 20 2163 Navrotsky et al. [1989] FezSi04 (Fa) 89.3 ± 1.1 1490 Stebbins and Carmichael [1984]

206 L. MATILE et at.: Chapter 6

The experimentally determined latent heats for magmatic minerals at their melting temperature (Tf) are given in Table A.3. If the melting temperatures (Tf) are significantly higher than the glass transition temperatures then an additional term for integration of heat capacity is needed [e.g., Richet and Bottinga, 1986; Lange and Carmichael, 1990].

The latent heat of crystallisation of magmatic minerals (L, kJ/kg) are plotted in Fig. AI, panel A. as a function of temperature (T, DC) extrapolated using the appropriate integration of heat capacity (melts from Lange and Navrotsky [1992], glasses from Stebbins et al. [1984]).

The latent heat of melting of crustal rocks (Fig. AI, panel B) was calculated for the normative magmatic minerals of less fertile tonalite (T, Rutter and Wyllie [1988]) and more fertile pelite (P, Vielzeuf and Holloway [1988]) for completely molten compositions for f = 1 and also forf= 0.5 (Ta, Th, Pa, Ph)'

soo

L600

[kJ/kg]

400

200

A B 350

300 L [kJ/kg]

250

200

Figure A.i. The latent heat of crystallisation (L, kJ/kg) plotted as a function of temperature (T, 0c) for magmatic minerals (panel A) and for assimilates (panel B, pelite (P), tonalite (T».

APPENDIX 3. PHYSICAL PARAMETERS

Table A.4. Physical parameters, their values and some definitions of the thermal AFC model

M(/,Mci

M/o Mm i

Mm(Ji

assimilated and crystallised masses during AFC step i crystallised mass during step i without any influence by assimilation mass of the mantle melt before step i mass of the mantle melt after the hybridisation with the assimilate (i.e. Mmi

+M,/) mass of the parental mantle magma temperature of the parental mantle magma (1 350°C)

Tmi

Ll Tm Tao T,/ ew em Lm Lm f

6. Fractionation Model/or Hydrous Calc-Alkaline Plutons

temperature of the mantle magma after step i (900-1 350°C) temperature interval of one AFC step (lODC) ambient country rock temperature (200-800°C) segregation temperature of the assimilate (900°C) heat capacities of assimilate and assimilant (1.0-1.2,1.3-1.5 kJ/kgK) latent heats of crystallisation (0.2 - 0.6 MJlkg, Fig. 4 and A.l) melt fraction (wt.) in the country rock fraction of crystals in the magma latent heat of fusion of the mantle magma (10 - 20 kJlkg, Fig. 5)

207

cPx

LlH"tu, LlHmliq heat contribution to LlHmi from cooling the mantle melt (l2 - 15 kJ/kg, Fig.

5) LlH xtal

m

r

F

heat contribution to LlHmi from cooling the crystals in the mantle magma (0 - 10 kJ/kg, Fig. 5) ratio of assimilated and crystallised masses, i.e. r = MaiM" relative mass of mantle melt, i.e. F = MmiIMm".

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