Do Boundary Layers Affect the Compositions of Melt Inclusions? No! Fedele Luca1, Cannatelli Claudia2, Bodnar Robert J.1, Severs Matthew31) Dept. of Geosciences, Virginia Tech, Blacksburg VA 24061 lfedele@vt.edu, rjb@vt.edu2) Institute of Crustal Studies, University of California Santa Barbara, CA 93106 claudiac@vt.edu3) Dept. of Geology, College of Wooster, 1189 Beall Avenue, Wooster, OH 44691 MSevers@wooster.edu

Melt Inclusions (MIs) trap small amounts of melts during crystal growth, isolating it from the crystallizing magma and preserving important information on the magmatic

history of an igneous system. They represent an unique opportunity to gather direct information of the composition of melts from which the host crystal grew, and for this reason

MIs use in petrology has steadily increased during the years, up to the point that now MIs are used routinely as source of chemical information on the evolution of magmas.

With the increasing amount of information available on MIs, it became evident that some processes occurring either during crystal growth, or after MIs entrapment, can

potentially compromise MIs composition, making it fairly different from the surrounding melt. In particular some workers argued that chemical gradients that develop at the

crystal/melt interface during crystal growth, as consequence of preferential incorporation of some elements in the crystal, form boundary layers (BL) that, if trapped, could affect

MIs composition especially with regard to minor and trace elements.

Elements that are incompatible in the host phase become enriched in the BL, while elements compatible with the host are depleted, compared to the “far-field” melt. The

thickness of the BL, and the chemical gradients that develop inside its boundaries, are function of both the crystal growth rate and the diffusion rate of each element, while the

enrichment/depletion profiles will decay exponentially as function of the distance from the crystal/melt interface. MIs that trap aliquots of the BL will show stronger enrichment

in incompatible elements (or stronger depletion in compatible ones) as function of the inverse of their size, since smaller inclusions will trap a smaller “thickness” of the BL melt

(Fig. 1).

While some studies suggest that the BL does not affect MIs larger that 50 mm (Lu et al., 1995), there is no available information concerning the minimum size MI that can be

analyzed before BL processes produce a measurable effect on its composition. Nowadays advances in analytical techniques have reduced the “workable” size for MIs, and

instrumentations such as the laser-ablation microprobe (LA-ICPMS) or the ion probe (SIMS) can analyze MIs as small as 10 µm, making of paramount importance to ascertain if

such small MIs can be used as reliable source of information on the chemistry of magmas.

Effects of boundary layer have been reported at first for glass rims around crystals, in natural and synthetic systems (Albarede & Bottinga, 1972; Donaldson, 1975; Peterson

& Lofgren, 1986; Muncill & Lasaga, 1987; Aoki, 1993), and a model for boundary layer effect was proposed by Bacon (1989) to account for the common occurrence of accessory

minerals as solid phase inclusions in major rockforming minerals in felsic to intermediate composition.

Sobolev (1996) pointed out that the coexistence in a single crystal of MIs displaying a large range of trace elements concentrations suggests disequilibrium conditions, and

hence that those MIs might have had their original composition altered by diffusion during entrapment. Concerns regarding the effect that BL could have on MIs were reviewed

by Anderson (2003), who pointed out that “Melt inclusions necessarily sample local near-crystal microenvironments.”, but that despite the fact that local variations can be relevant

(Anderson & Wright, 1972), they often correlate well from crystal to crystal (Watson 1976).

Faure & Schiano (2005) conducted experiments on forsterite crystallization, to study the mechanisms of melt inclusion formation and the relationships of their compositions

in relation to crystal morphology. They concluded that trapping of MIs in dendritic or skeletal forsterite crystals is controlled by diffusion, and consequently that those MIs trap

consistent portions of the boundary layer, resulting in compositions quite different from the bulk magma. On the other hand, MIs in trapped in polyhedral crystal, form when

“interface attachment processes control the rate of crystal growth” and represent the composition of the bulk melt.

In this study we measured abundances of 23 major, minor and trace elements in quartz-hosted MIs from the Bishop Tuff (CA), and olivine-hosted MIs from Mauna Loa

(Hawaii) by LA-ICPMS. The rationale behind the choice of these particular samples is explained in the following sections.

Purpose of the study is not to assess if boundary layer processes can affect the composition of a melt adjacent to a growing crystal, but rather to evaluate what effect (if any)

compositional gradients and boundary layer can have on the composition of melt inclusions so to make them not representative of the far-field melt. The discussion will be limited

to the boundary layer problem, and we will not discuss post-entrapment modification of MIs.

INTRODUCTIONDiffusion data (i.e. diffusion coefficients) can be obtained either by experiments (Ryerson, 1987), or by modeling (Fortier & Giletti, 1989). An useful review of the role of

diffusion in geologic systems can be found in Watson & Baxter (2007, and references therein), while compilations of diffusion coefficients for silicate minerals, glasses and liquids,

are given by Freer (1981) and Brady (1995).

Crystal/melt partition coefficients, gathered from experimental studies (Lindstrom & Weill, 1978; Beattie et al., 1991; Keppler & Wyllie, 1991), from phenocryst/matrix

analysis (Onuma et al., 1968; Higuchi & Nagasawa, 1969; Jones & Layne, 1997), and melt inclusions/host pairs analysis (Thomas et al., 2002; Severs et al, 2007; Petrelli et al.,

2007; Zajacz et al., 2008), are widely available in the literature (Irving, 1978; Jones, 1995, and references therein) and from online databases (Geochemical Earth Reference Model,

GERM). However partition coefficients are usually strongly dependent upon physical and chemical parameters, hence their use has to be paired with a critical examination of the

source, in order to determine the relevance to the specific problem.

A great amount of research has been conducted on the mechanisms of crystal growth, both from the theoretic and experimental viewpoint. While the bulk of the early studies

relates mostly to the field of material science, the interest in the particular aspects of crystal growth in geologic systems (i.e. multicomponents system) grew rapidly and theoretical

treatment (Lasaga, 1982) as well as experimental work (Muncill & Lasaga, 1987; Ihinger & Zink, 2000) and studies on magma residence times (Christensen & DePaolo, 1993;

Turner et al., 2003) followed. A useful theoretical and experimental review can be found in Kirkpatrick (1975).

However crystal growth rates reported in literature are usually poorly constrained and can vary several orders of magnitude. For instance reported quartz growth rates in silicic

melts range from 10-6 to 10-11 cm/s (Swanson, 1977; Brandeis & Jaupert, 1987; Cashman, 1988), while for olivine growth rates can vary from 10-5 to 10-8 cm/s (Donaldson, 1975;

Armienti et al., 1991; Jambon et al., 1992).

To understand the potential effects of the boundary layer buildup on MIs composition, we used equation (5) to model the variations in concentration of selected incompatible

and compatible elements at the crystal/melt interface for quartz and olivine; in all calculations a concentration of 100 ppm was used to make it easier to recognize element

enrichment/depletion.

As pointed out by Lasaga (1981) the boundary layer thickness (δ in equations 3 and 4), is directly related to the ratio d/R, and when δ >> d/R then the boundary layer itself

becomes unimportant. In fact the concentration at the crystal/melt interface becomes significantly different only within a distance defined as d/R (i.e. the characteristic length of

the steady state constant growth system, Albarede & Bottinga, 1972).

Lasaga (1981) expressed the time required to buildup a boundary layer of thickness d/R, considering that any component will diffuse in a melt for a distance in a time

t, while the same component will travel a distance Rt relative to the crystal/melt interface. This relationship between diffusion and growth rate implies that the limit of the boundary

layer is defined by , or . This is the time required to build up a steady state boundary layer at a given R and d.

We examined different scenarios, to investigate the evolution of the boundary layer as function of time and growth rates. Figure 2 and 3 show the calculated concentration

profiles (i.e. concentration vs. distance from the crystal/melt interface). The plots allow to highlight the following points:

1) with fixed R and d, increasing time yields steeper concentration profiles. The maximum enrichment in incompatible elements compared to the concentration in the far-field

melt (or depletion in compatible ones) increases very fast, as well as the boundary layer thickness;

2) increasing R at fixed d (and recalculating the time t according to ) yields steeper concentration profiles. However maximum enrichment in incompatible elements

(or depletion in compatible ones) remains constant while the boundary layer thickness decreases very fast;

3) at low R boundary layer thickness appears to be larger as well as the time required to build up a steady state boundary layer.

THE BOUNDARY LAYER PROBLEM - IStudies on the boundary layer were first prompted by the need of explaining element zoning in crystals, which required modeling the trace elements behaviour in melts. Initially

they relied on mathematical models developed for metallurgical purposes to study the behaviour of impurities in metals, such as those of Tiller et al. (1953) and Smith et al. (1955).

Later work, such as that of Lu et al. (1995), explicitly applied the mathematical treatment to the case of melt inclusions. We will review some of the classical models, and use their

proposed solutions to the diffusion equation to express the quantitative variation of trace elements at the crystal/melt interface during melt inclusion formation.

Elements enter the lattice based on their partition behavior during crystal growth, but diffusion in a magma is usually too slow to maintain an homogeneous melt phase next to

the growing crystal (Bottinga et al., 1966), and as a consequence some elements will become enriched or depleted near the crystal/melt interface. Concentrations of these elements

at the interface can be extremely different from the concentrations in the “far-field” melt, since any convection or motion in the magma that could potentially reduce the chemical

gradients will disappear in proximity of the crystal face, therefore leading to the formation, next to the growing crystal, of a boundary layer (Burton et al., 1953).

The characteristics of the boundary layer, its thickness and the intensity of the concentration gradients inside, are mainly functions of the crystal growth rate, of the elemental

diffusion and of the elemental partition behavior. Numerical models that take into account these parameters have been developed based on the modeled mechanisms of crystal

growth.

Burton et al. (1953) studied crystallization as an heterogeneous reaction where element incorporation (or rejection) into the solid phase is characterized by an equilibrium

partition coefficient k0 = C

S / C

L [where C

S = element concentration in the solid; C

L = element concentration in the bulk liquid (i.e. far-field melt)], which can vary during

crystallization due to the contribution of element transport processes by diffusion in the melt. Assuming that transport occurs in a one dimensional, steady state laminar fluid flow,

and that beyond a distance δ (i.e. the boundary layer thickness) from the growing interface the fluid flow keeps the concentration uniformly equal to CL, Burton et al. (1953)

proposed a particular solution of the continuity equation (not shown, see eq. 2 in Burton et al., 1953) and showed that the concentration at the interface (Ci) is:

)1( dfSL

dfi eCCeC δ δ −+=

Lasaga (1981) examined the model of Burton et al. (1953) and proposed a more general solution for the continuity equation at the steady state, with the explicit incorporation

of a constant partition coefficient k (where k = CS / CL; R = constant growth rate; d = diffusion rate; x = distance from the crystal/melt interface; C0 = concentration in the bulk

melt (i.e. far-field melt): δ = boundary layer thickness.:

f = growth rate (constant); d = diffusion rate (constant).

BxdRAxC +

−−= exp1)(

( )( )

−−+

−=

dRkk

CkAδexp1

1 0

( )

−−+

=

dRkk

CBδexp1

0

(1)

(2) (3) (4)

(5)

Smith et al. (1955) investigated the redistribution of solute occurring during solidification of a single phase alloy, and developed a solution of the one-dimensional diffusion

equation that takes into account transient states. This time-dependent solution was derived under the assumptions that: 1) diffusion in the solid phase is negligible; 2) convective

mixing in the melt is negligible; 3) the distribution coefficient k is constant; 4) the crystal/melt interface is plane and perpendicular to the direction of crystal growth. The solution

allows to model the build up of the region of high solute concentration (i.e. the boundary layer) next to the crystal/melt interface, including the rise of concentration leading to the

steady state (where k = mineral/melt partition coefficient; R = constant growth rate; d = diffusion rate; erfc = complementary error function):

( ) ( ) ( )

+−

−

−+= − RtxdterfcRtxdterfce

kkCC xdR

L )(121

21)(1

21

2)1(10

( )( ) ( )( )

−+

−

−−

+ +−− Rtkxdterfcekk

k kRtxdRk 12)(1211

11

21 )1(

Equations (2) and (5) can all be used to model element distribution near the crystal/melt interface when diffusion is the dominant mechanism of mass transfer of components

towards and away from the crystal surface. To carry out such modeling it is necessary the availability of data (or estimates) on: a) concentration of the element in the far-field melt

(C0); 2) diffusivity of the element in the melt (d); 3) element crystal/melt partition coefficient (k); 4) crystal growth rate (R).

While concentration in the far-field melt (C0) can be reasonably well constrained using, for instance, elemental abundance in large MIs (≥ 50 mm, which can be safely assumed

as representative of the far-field melt, Lu et al., 1995), elemental diffusivities, crystal/melt partition coefficients and crystal growth rates, are somewhat more difficult to acquire.

THE BOUNDARY LAYER PROBLEM - II

Samples were selected to test whether the composition of MIs trapped in growing crystals might be affected by BL and not be representative of the composition of the far-field

melt. We studied the composition of several tens of glassy quartz-hosted MIs from the Bishop Tuff (CA), and olivine-hosted MIs from Mauna Loa (Hawaii), both to focus on the

size vs. composition relationship (analyzed MIs range from few microns up to several hundred microns in length) and to investigate MIs behavior in a wide range of melts (i.e.

rhyolite vs. basalt). Following is a brief description of each sample suite.

Bishop Tuff

The Bishop Tuff (BT) formed 760 ka ago, during the large Quaternary eruptions of the Long Valley magma chamber in eastern California, which lasted for about 6 days. They

consist mainly of ash and pumice clasts of high silica rhyolite, bearing crystals of biotite, plagioclase, quartz and sanidine. Eruptive volume has not been completely defined, but

Hildreth & Wilson (2007), which give a thorough review of the characteristics of the BT, estimate it at 600 ÷ 650 km3. Hildreth (1979) and Halliday et al. (1984) were the first to

recognize and investigate chemical zoning in the BT, which was later confirmed by melt inclusions studies such as those of Anderson et al. (2000).

We selected melt inclusion in quartz phenocrysts separated and hand picked from individual pumice clasts collected from unit IG2E of Wilson and Hildreth (1997). MIs are

analogous to those studied by Anderson et al. (2000), which allowed a comparison of our analytical results with those available in the literature.

All analyzed MIs were glassy, mainly spherical in shape, and did not require any re-heating before analyses, they ranged in size from 8 to 100 µm. Melt inclusions cracked or

containing solids were readily identified and carefully avoided during analysis.

Mauna Loa

Hawaiian islands are among the best studied volcanic islands in the world. Those volcanoes typically evolve in 4 stages, each one characterized by different chemical

composition of the erupted products as well as supply rate and degree of mantle melting (Clague, 1987). The Mauna Loa volcano is at the shield stage and its products are

dominated by tholeiitic basalt, indicative of a fairly high magma supply, large degree of mantle melting, and of a shallow magma plumbing system. Detailed information on the

Mauna Loa eruptive history can be found in Barnard (1990, 1991, 1992), while a review of geochemical and petrological information is given by Muir & Tilley (1963).

We selected olivine phenocrysts from Mauna Loa lavas, similar to those “normal” (i.e. non Sr-rich) analyzed by Sobolev et al. (2000). MIs were all glassy, from spherical to

elongated in shape and ranged in size from 9 to 700 µm. Melt inclusions cracked or containing solids were readily identified and carefully avoided during analysis. No evident

petrographic sign of olivine precipitation on melt inclusions wall were detected.

Analytical techniques

MIs in quartz phenocrysts from the Bishop Tuff and in olivine phenocrysts from the Mauna Loa, were mounted in one inch epoxy mount and polished to expose the glassy

inclusion for analyses. To minimize the possibilities of bias, after a first set of analysis each mount was repolished to expose MIs from greater depth inside the phenocrysts, and

further analyses were carried on. Major, minor and trace elements were analyzed at Virginia Tech using a Laser Ablation ICPMS system with a 193 nm ArF Excimer laser

(GeoLasPro) coupled with a quadrupole mass spectrometer equipped with reaction cell technology (Agilent 7500ce) to minimize interferences. Data were reduced using the

software AMS (Mutchler et al., 2008) using normalization to 100% oxides.

SAMPLES AND ANALYTICAL TECHNIQUES

Bishop Tuff

MIs in quartz from the BT were analyzed for 23 major and trace elements (Al, B, Ba, Ca, Ce, Fe, Gd, K, Li, Mg, Mn, Mo, Na, Nb, Ni, Pb, Rb, Si, Th, Ti, Y, Yb, Zr). Selected

major and trace elements analysis of BT melt inclusions are plotted vs. inclusions size and compared with ranges from Anderson et al. (2000) in Fig. 5.

Results can be summarized as follows:

1) Major and trace elements concentrations in MIs compare quite well with the results of Anderson et al. (2000), with the partial exception of Al, Ti, Nb, Ca (not shown) and Mn

(not shown);

2) No apparent correlation has been found between element concentration and inclusion size.

Mauna Loa

MIs in olivine from Mauna Loa were analyzed for 22 major, minor and trace elements (Al, Ba, Ca, Ce, Co, Cr, Dy, Fe, Gd, K, Mg, Mn, Na, Ni, Rb, Si, Sr, Ti, U, Y, Yb, Zr).

Selected major and trace elements analysis of ML melt inclusions are plotted vs. inclusions size and compared with ranges from Sobolev et al. (2000) in Fig. 6.

Results can be summarized as follows:

1) Major and trace elements concentrations in MIs compare quite well with the results of Sobolev et al. (2000), with the partial exception of Ca and Y;

2) No apparent correlation has been found between element concentration and inclusion size.

RESULTSWe analyzed melt inclusions in quartz and olivine ranging in size from 8 to 100 and 9 to 700 mm respectively, in order to investigate possible anomalous enrichment in

incompatible or depletion in compatible elements respect to the far-field melt that can be ascribed to boundary layer effect. According to mathematical modeling of the boundary

layer build up, carried out using the model of Smith et al. (1955), and to the findings of Lu et al. (1995), melt inclusions that trap aliquots of the boundary layer should show a

correlation between inclusions size and element concentration. In particular small inclusions would trap a larger “thickness” of the boundary layer relatively to their size (Fig. 1)

and consequently they would show a greater enrichment in incompatible elements or a greater depletion in compatible ones.

The results of our analysis show no evident correlation between melt inclusion size and element concentration, suggesting that even inclusions as small as 10 mm can be

representative of the far-field melt composition. We suggest that boundary layer development did not affect the MI investigated in this study, possibly because the rate of crystal

growth was slow relative to diffusive transport of elements in the melt. Since this might not always be the case, our findings suggest that the size vs concentration criteria can be a

useful and simple first level approach to test the boundary layer effects on melt inclusions.

However it is important to point out that processes other than the boundayr layer can affect melt inclusions composition (i.e. post intrapment modifications), and that any

“anomalous” melt inclusion composition has to be investigated taking in consideration all the possible causes and integrating any findings in the general petrological contest of the

samples under study. This part of our research focused only on possible boundary layer effects, and further work is near completion to integrate these findings with a more

comprehensive approach to the problem of compositional modifications that can affect melt inclusions during and after their trapping.

FINAL REMARKS

dt

Rtdt = 2/ Rdt =

Distance (cm)

0.00 0.02 0.04 0.06 0.08 0.10

50

100

150

200

250

300

Rb (p

pm

)Rb

(pp

m)

t = d/R2 = 4.4 x 103 s

R = 3 x 10-6

k = 0.014c = 100

tt x 10t x 100

d = 3.98 x 10-8

0.000 0.002 0.004 0.006 0.008 0.010

50

100

150

200

250

300

RR x 10R x 100

k = 0.014c = 100 t = d/R2

B

D

0 20 40 60 80 100

100

150

200

250

300t = d/R2

k = 0.01c = 100

t = 11.5 days

t = 2.7 hrs

t = 100 s

pp

mp

pm

Distance (mm)

R = 10-8

d = 10-10

RR x 10R x 100

0 20 40 60 80 100

50

100

150

200

t = d/R2

k = 10c = 100

R = 10-8

d = 10-10

RR x 10R x 100

A

B

distance

conc

entra

tion

crys/melt interfaceboundary layer thickness

element conc.

increas. conc. in MIs

2/ Rdt =

Fig. 2 - Boundary Layer build up as function of R (growth rate) and t (time) in Olivine for incompatible (Ba) and compatible (Ni) elements.

Olivine

Quartz Generic

Fig. 5 - Bishop Tuff Quartz. Plots of element vs MIs size. Red arrows are concentration ranges from Anderson et al. (2000)

Fig. 6 - Mauna Loa Olivine. Plots of element vs MIs size. Red arrows are concentration ranges from Sobolev et al. (2000)

Fig. 4 shows a concentration profile as function of growth rate for a generic host and a generic incompatible (Fig. 4a) and compatible (Fig. 4b) element. Partition and diffusion

coefficients and growth rate were selected in order to generate a profile and a boundary layer at a micrometric and temporal scale compatible with melt inclusion formation. In this

case BL build up occurs in short period of times (from 100s of second to few days), and its thickness extends up to several tens of microns.

Based on the results of the modeling it is likely that during rapid crystal growth boundary layer can form at the crystal/melt interface, where higher concentrations of incompat-

ible elements (or lower concentrations of compatible ones) respect to the far-field melt can be found.

MIs trapped within the time frame of these growth episodes, could potentially reflect the elemental concentrations of these boundary layers as function of MIs size (Fig. 1),

but also as function of the boundary layer characteristics, which in turn are dependent from R, d, k and t. It is then reasonable to expect that MIs affected by BL and trapped in mul-

tiple co-precipitating mineral phases, would present different degrees of enrichment in incompatible elements (or depletion in compatible ones). Finally positive correlations are

to be expected between incompatible elements in MIs that trap significant portions of the BL (Lu et al., 1995).

0.0 0.1 0.2 0.3 0.4

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0

200

400

600

800

1000

1200

1400

R = 6 x 10-7

d = 10-7

t = d/R2 = 3 x 105 s

tt x 10t x 100

k = 0.03

c = 100

RR x 10R x 100

t = d/R2

Ba

(pp

m)

Ni (

pp

m)

Ba

(pp

m)

Distance (cm)

0 10 20 30 40

20

40

60

80

100

120

140

R = 6 x 10-7

d = 7.2 x 10-6

t = d/R2 = 2 x 107 s

tt x 10t x 100

k = 12.2

c = 100

0 5 10 15 20 25 30

20

40

60

80

100

120

140

RR x 10R x 100

t = d/R2

k = 12.2

c = 100

k = 0.03

c = 100

Distance (cm)

A C

B D

0

20

40

60

80

100

120

140

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Li (p

pm)

0

40

80

120

160

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

B (p

pm)

0

100

200

300

400

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Mg

(ppm

)

55000

60000

65000

70000

75000

80000

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Al (

ppm

)

250

300

350

400

450

500

550

600

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Ti (p

pm)

90

130

170

210

250

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Rb

(ppm

)

10

15

20

25

30

35

40

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Nb

(ppm

)

0

5

10

15

20

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Gd

(ppm

)

10

15

20

25

30

35

40

0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1

Log Size (µm)

Th (p

pm)

0

40

80

120

160

200

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Ba

(ppm

)

0

10

20

30

40

50

60

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Ce

(ppm

)

0

100

200

300

400

500

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Sr (p

pm)

0

40

80

120

160

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Zr (p

pm)

40

50

60

70

80

90

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Ca

(ppm

) x 1

000

4

6

8

10

12

14

16

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Ti (p

pm) x

100

0

0

2

4

6

8

10

12

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Dy

(ppm

)

0

5

10

15

20

25

30

35

40

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Y (p

pm)

0

1

2

3

4

5

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Log Size (µm)

Yb (p

pm)

Albarede, F., and Bottinga, Y. (1972). Kinetic disequilibrium in trace element partitioning between phenocrysts and host lava. Geochim. Cosmochim. Acta, 36:141-156.Anderson A.T. (2003). Melt (glass ± crystals) inclusions. In: I. Samson, A. Anderson, and D. Marshall, Eds. Fluid Inclusions: Analysis and Interpretation, 32, p. 300. MAC Short Course series, Ottawa.Anderson A.T. and Wright T.L. (1972). Phenocrysts and glass inclusions and their bearing on oxidation and mixing of basaltic magmas, Kilauea volcano, Hawaii. Am. Mineral., 57:188-216.Anderson A.T., Davis A.M. & Lu F. (2000). Evolution of Bishop Tuff Rhyolitic Magma Chamber Based on Melt and Magnetite Inclusions and Zoned Phenocrysts. J. Petrol., 41(3): 449-473.Aoki, Y., and Iyatomi, N. (1993). Concentration gradients in CaAl2Si2O8 melt near the crystals-melt interface. N. J. fur Min.: Monatshefte, 8:374-384.Bacon C.R. (1989). Crystallization of accessory phases in magmas by local saturation adjacent to phenocrysts. Geochim. Cosmochim. 53:1055-1066.Barnard W. M. (1990). Mauna Loa – A Source Book. Historical Eruptions and Exploration. Volume One: From 1778 through 1907. Walther M. Barnard, Fredonia, N.Y. Pub.Barnard W. M. (1991). Mauna Loa - A Source Book. Historical eruptions and exploration. Volume Two: The early HVO and Jaggar years (1912-1940). Walther M. Barnard, Fredonia, N.Y. Pub.Barnard W. M. (1992). Mauna Loa - A Source Book. Historical eruptions and exploration. Volume Three: The post-Jaggar years (1940-1991). Walther M. Barnard, Fredonia, N.Y. Pub.Beattie P., Ford C. and Russell D. (1991). Partition coefficients for olivine-melt and orthopyroxene-melt systems. Cont. Mineral. Petrol., 109:212-224.Bottinga Y., Kudo A. and Weill D. (1966). Some Observations on Oscillatory Zoning and Crystallization of Magmatic Plagioclase. Am. Mineral., 51:792-806.Brady J.B. (1995). Diffusion Data for Silicate Minerals, Glasses and Liquids. In: Mineral Physics and Crystallography. Handbook of Physical Constants Vol. 2, AGU Reference Shelf, p. 269-290.Brandeis G. and Jaupert C. (1987). The kinetics of nucleation and crystal growth and scaling laws for magmatic crystallization. Contrib. Mineral. Petrol., 96:24-34.Burton J.A., Prim R.C. and Slichter W.P. (1953). The Distribution of Solute in Crystals Grown from the Melt. Part I. Theoretical. J. Chem. Phys., 21:1987-1991.Cashman K.V. (1988). Crystallization of Mount St. Helens 1980-1986 dacite; a quantitative textural approach. Bull. Volc., 50:194-209.Christensen J. N. and DePaolo D. J. (1993). Time scales of large volume silicic magma systems; Sr isotopic systematics of phenocrysts and glass from the Bishop Tuff, Long Valley California. Contrib. Mineral. Petrol., 113:100-114.Clague D.A. (1897). Hawaiian xenolith populations, magma supply rates, and development of magma chambers. Bull. Volcanol., 49:577-587.Donaldson C.H. (1975). Calculated diffusion coefficients and the growth rate of olivine in a basalt magma. Lithos, 8(2):163-174.Donaldson, D.H. (1975). Calculated diffusion coefficients and the growth rate of olivine in a basalt magma. Lithos, 8:163-174.Faure F. and Schiano P. (2005). Experimental investigation of equilibration conditions during forsterite growth and melt inclusion formation. EPSL, 236:882– 898.Fortier S.M. and Giletti B.J. (1987). An Empirical Model for Predicting Diffusion Coefficients in Silicate Minerals. Science, 245(4925):1481-1484.

Freer B. (1981). Diffusion in silicate minerals and glasses: A data digest and guide to the literature. Cont. Mineral. Petrol., 76(4):440-454.Geochemical Earth Reference Model (GERM) - http://earthref.org/GERM/ - Albarede F, White W. and Staudigel H., curators.Halliday A.N., Fallick A.E. Hutchinson J. & Hildreth W. (1984). A Nd, Sr, and O isotopic investigation into the causes of chemical and isotopic zonation in the Bishop Tuff, California. EPSL, 68:379-391.Higuchi H. and Nagasawa H. (1969). Partition of trace elements between rock-forming minerals and the host volcanic rocks. EPSL, 7:281-287.Hildreth W. (1979). The Bishop Tuff: evidence for origin of compositional zonation in silicic magma chambers. In: Chapin C.E. & Elston W.E. (eds) Ash-flow tuffs. Geological Society of America, Special Paper 180:43-75.Hildreth W. and Wilson C.J.N., (2007). Compositional Zoning of the Bishop Tuff. J. Petro., 48(5): 951-999.Ihinger P.D. and Zink S.I. (2000). Determination of relative growth rates of natural quartz crystals. Nature, 404:865-869.Irving A.J. (1978). A review of experimental studies of crystal/liquid trace element partitioning. Geochim. Cosmochim. Acta, 42:743–770.Jones J.H. (1995). Experimental Trace Element Partitioning. In: Rock Physics and Phase Relations. Handbook of Physical Constants Vol. 3, AGU Reference Shelf, p. 73-104.Jones R.H. and Layne G.D. (1997). Minor and trace element partitioning between pyroxene and melt in rapidly cooled chondrules. Am. Mineral., 82(5-6):534-545.Keppler H. and Wyllie P. J. (1991). Partitioning of Cu, Sn, Mo, W, U, and Th between melt and aqueous fluid in the systems Haplogranite–H2O-HCl and Haplogranite–H2O-HF. Contrib. Mineral. Petrol., 109:139–150.Kirkpatrick R.J. (1975). Crystal Growth from the Melt: A Review. Am. Mineral., 60:798-814.Lasaga A.C. (1981). Implications of a concentration-dependent growth rate on the boundary layer crystal-melt model., EPSL, 56:429-434.Lasaga A.C. (1982). Toward a master equation in crystal growth. Am. J. Sc., 282:1264-1288.Lindstrom D.J. and Weill D.F. (1978). Partitioning of transition metals between diopside and coexisting silicate liquids. I. nickel, cobalt and manganese. Geochim. Cosmochim. Acta, 42:817-831.Lu F., Anderson A.T. and Davis M.D. (1995). Diffusional Gradients a the Crystal/Melt Interface and Their Effect on the Composition of Melt Inclusions. J. Geol., 103:591-597.Muir I.D. & Tilley C.E. (1963). Contributions to the petrology of Hawaiian basalts; [Part] 2, The tholeiitic basalts of Mauna Loa and Kilauea, with chemical analyses by J. H. Scoon. Am. J. Science, 261(2):111-128.Muncill G.E. and Lasaga A.C. (1987). Crystal-growth kinetics of plagioclase in igneous systems: One atmosphere experiments and application of a simplified growth model. Am. Mineral., 72:299-311.Muncill, G.E., and Lasaga, A.C. (1987). Crystal growth kinetics of plagioclase in igneous systems: one atmosphere experiments and application of a simplified growth model. Am. Mineral., 72:299-311.Mutchler S.R., Fedele L. & Bodnar R.J. (2008). Analysis Management System (AMS) for reduction of laser ablation ICPMS data. (in press).Onuma N., Higuchi H., Wakita H. and Nagasawa H. (1968). Trace element partition between two pyroxenes and the host lava. EPSL, 5(1):47-51.

Peterson, J.S., and Lofgren, G.E. (1986). Lamellar and patchy intergrowths in feldspar: experimental crystallization of eutectic systems. Am. Mineral., 71:343-355.Petrelli M., Caricchi L. and Ulmer P. (2007). Application of High Spatial Resolution Laser Ablation ICP-MS to Crystal-Melt Trace Element Partition Coefficient Determination. Geost. Geoan. Res., 31(1):13-25.Ryerson F.J. (1987). Diffusion measurements: experimental methods. Methods Exp. Phys., 24A:89-30.Severs M.J., Mutchler S.R., Bodnar R.J. and Beard J. (2007). Distribution of trace elements (ree, Sr, Ba, Y, Ti, Zr, HF, Nb, Pb) between dacitic melt, plagioclase, orthopyroxene, and clinopyroxene: evidence from silicate melt

inclusions. Abstracts with Programs - Geological Society of America, vol. 39, no. 6, pp.389.Smith V.G., Tiller W.A. and Rutter J.W. (1955). A Mathematical Analysis of Solute Redistribution During Solidification. Can. J. Phys., 33:723-744.Sobolev A.V. (1996). Melt inclusions in minerals as a source of principle petrological information. Petrology, 4:209–220.Sobolev A.V., Hofmann A.W. & Nikogosian I.K. (2000). Recycled oceanic crust observed in ‘ghost plagioclase’ within the source of Mauna Loa lavas. Nature, 404:986-990.Swanson S.E. (1977). Relation of nucleation and crystal-growth rate to the development of granitic textures. Am. Mineral., 62:966-978.Thomas J.B. & Bodnar R.J. (2002). A technique for mounting and polishing melt inclusions in small (<1 mm) crystals. Am. Mineral., 87:505-508.Thomas J.B., Bodnar R.J., Shimizu N. and Sinha A.K. (2002). Determination of zircon/melt trace element partition coefficients from SIMS analysis of melt inclusions in zircon. Geochim. Cosmochim. Acta, 66(16):2887-2901.Tiller W.A., Jackson W.A., Rutter J.W. and Chalmers B. (1953). The redistribution of solute atoms during the solidification of metals. Acta Metall., 1:428-437.Turner S, George R., Jerram D.A., Neil Carpenter N. and Hawkesworth C. (2003). Case studies of plagioclase growth and residence times in island arc lavas from Tonga and the Lesser Antilles, and a model to reconcile

discordant age information. EPSL, 214:279-294.Watson B. and Baxter E.F. (2007). Diffusion in solid-Earth systems. EPSL, 253:307-327.Watson E.B. (1976). Glass inclusions as samples of early magmatic liquids: determinative method and application to a South Atlantic basalt. J. Volcanol. Geotherm. Res., 1:73-84.Wilson C.J.N & Hildreth W. (1997). The Bishop Tuff: new insights from eruptive stratigraphy. J. Geol., 105:407-439.Zajacz Z., Halter W.E., Pettke T. and Guillong M. (2008) Determination of fluid/melt partition coefficients by LA-ICPMS analysis of co-existing fluid and silicate melt inclusions: Controls on element partitioning. Geochim.

Cosmochim. Acta, 72:2169–2197.

Fig. 1 - Melt inclusions that trap aliquots of the boundary layer should show stronger enrichment in incompatible elements as function of the inverse of their size, since smaller inclusions will trap a smaller “thickness” of the boundary layer melt

Fig. 3 - Boundary Layer build up of Rb in Quartz as func-tion of R (growth rate) and time.

Fig. 4 - Boundary Layer build up for a generic element in a genereric host as function of R (growth rate) and time.