evaporation and condensation during cai and chondrule formation

Chondrites and the Protoplanetary Disk

ASP Conference Series, Vol. 341, 2005 A. N. Krot, E. R. D. Scott, & B. Reipurth, eds.

432

Evaporation and Condensation During CAI and Chondrule For-mation A. M. Davis

Chicago Center for Cosmochemistry, Enrico Fermi Institute, and Department of

the Geophysical Sciences, The University of Chicago, 5640 South Ellis Avenue,

Chicago, IL 60637, USA

C. M. O’D. Alexander

Department of Terrestrial Magnetism, Carnegie Institution of Washington, 5241

Broad Branch Road, Washington, DC 20015, USA

H. Nagahara

Department of Earth and Planetary Sciences, University of Tokyo, Hongo, Tokyo

113-0033, Japan

F. M. Richter

Chicago Center for Cosmochemistry and Department of the Geophysical Sci-

ences, The University of Chicago, 5640 South Ellis Avenue, Chicago, IL 60637,

USA

Abstract. Evaporation and condensation played important roles in the high tempera-ture processing of nebular material that led to CAIs and chondrules. We review recent progress in modeling and laboratory simulation of volatility fractionation under nebu-lar conditions and their application to the bulk chemical and isotopic properties of natural CAIs, chondrules and micrometeorites.

1. Introduction

The most general argument for evaporation and condensation having played a sig-nificant role in determining the chemical properties of Solar System materials is based on the observation that all these materials are variously but systematically de-pleted in their more volatile elements relative to the bulk composition of condensable matter in the solar system. CAIs and chondrules are particularly valuable for gaining

Evaporation and Condensation during CAI and Chondrule Formation 433

insight into condensation and evaporation, because they preserve isotopic, chemical and textural evidence of these processes. Coupled with modeling and laboratory ex-periments, the properties of CAIs and chondrules provide marvelous opportunities for understanding the conditions under which high temperature processes occurred in the solar system.

Condensation and evaporation are terms widely used to describe volatility frac-tionation processes, but they are incomplete. It is important to distinguish between equilibrium and kinetically controlled processes. Condensation is usually used as shorthand for equilibrium fractionation with falling temperature, and evaporation is often taken to mean a kinetically controlled fractionation with increasing tempera-ture, but kinetically controlled condensation and near-equilibrium evaporation can also occur. Thermodynamic equilibrium condensation calculations have been widely applied for more than 30 years (Larimer 1967; Larimer & Anders 1967; Grossman 1972; Lewis, 1972; Grossman & Larimer 1974; Boynton 1975; Palme & Wlotzka 1976; Kelley & Larimer 1977; Wai & Wasson 1977; Davis & Grossman 1979; Larimer & Bartholomay 1979; Fegley & Lewis 1980; Fegley & Palme 1985; Wood & Hashimoto 1993; Yoneda & Grossman 1995; Petaev & Wood 1998; Ebel & Grossman 2000; Davis & Richter 2003; Lodders 2003). Significant advances in un-derstanding kinetically controlled evaporation processes are more recent (Hashimoto 1983; Hashimoto 1990; Davis et al. 1990; Alexander et al. 2000; Grossman et al. 2000; Nagahara & Ozawa 2000; Alexander 2001; Ozawa & Nagahara 2001; Alexan-der 2002; Richter et al. 2002; Grossman, Ebel, & Simon 2002; Davis & Richter 2003; Richter 2004; Alexander 2004). Volatility-based elemental fractionation can occur under equilibrium or kinetically-controlled conditions, whereas large isotopic mass fractionation effects can only occur under kinetic control. It is the presence or ab-sence of isotopic fractionation effects in CAIs and chondrules coupled with the con-ditions necessary to preserve these effects that constrain early Solar System environ-ments. Here, we review the theoretical background, relevant experiments, and appli-cations to CAIs and chondrules. This subject was recently reviewed by Davis & Richter (2003).

2. Theoretical Background

2.1. Evaporation

The evaporative flux from a solid or molten surface into a surrounding gas is given by the Hertz-Knudsen equation (see Hirth & Pound 1963),

J i nijJ ij

evapPijsat

2SmijRTj 1

n

¦ , (1)

where Ji is the flux of element or isotope i (moles per unit area per unit time), J ij

evap is the evaporation coefficient for the jth gas species containing i, nij is the number of at-oms of i in species j,

Pij

sat is the saturation vapor pressure of species j, mij is the mo-lecular weight of j, R is the gas constant, and T is the absolute temperature. The summation is over all gas species j containing i. Except for the evaporation coeffi-cients, the various quantities on the right-hand side of Eqn. 1 can be calculated given a suitable thermodynamic model for the condensed phase and for the composition

434 Davis et al.

and speciation in the surrounding gas. There is no formalism for calculating the evaporation coefficients, and thus these must be determined by laboratory experi-ments that we will discuss in later sections. Equation 1 gives a quantitative measure of evaporation rates only after the Jij values have been determined for the system of interest by combining laboratory data for Ji with a thermodynamic model for the speciation and saturation vapor pressures. Ji in Eqn. 1 is assumed to represent the flux from the surface whether or not recondensation is taking place. If there is a finite pressure of evaporating species in the gas at the surface of the condensed phase, the net evaporation rate (Ji,net) will be the difference between evaporation and reconden-sation, which can be written as,

J i,net nij J ij

evapPijsat � J ij

condPij� �2SmijRTj 1

n

¦ , (2)

where Pij is the pressure at the evaporating surface of the jth gas species containing the element or isotope i and

J ij

cond is the condensation coefficient. It is usually as-sumed that condensation coefficients are the same as the evaporation coefficients, which must be true at least in the limit

Pij o Pij

sat when equilibrium is approached. For the elements we will consider here, silicon, magnesium, iron and potassium,

the gas in equilibrium with liquids of solar or CAI-like compositions at high tempera-ture is usually dominated by a single species containing one atom of the element of interest: SiO, Mg, Fe and K. For these elements, n=1, nij=1 in Eqns. 1 and 2, which allows us to write a simpler version of Eqn. 2 in the form

J i,net J iPi

sat

2SmiRT

ª�

¬�

«�«�

º�

¼�

»�»�

1�Pi

Pisat

§�

©�¨�

·

¹¸

,

(3)

where J i J ievap J i

cond . The quantity in the square brackets is called the free evapora-tion flux and the net evaporation rate is simply the free evaporation rate reduced by a fraction Pi / Pi

sat . Equation 3 shows why vacuum evaporation experiments (limit

Pi / Pisat o 0) are used to determining evaporation coefficients in that the duration of

evaporation and the change in composition of the condensed phase gives a measure of Ji, while Pi

sat and mi can be calculated from the thermodynamics of the system, allowing determination of the only remaining unknown, J i

evap . Equation 3 remains valid for Pi / Pi

sat ! 1 , in which case the condensation flux will be greater than the evaporation flux and net effect will be condensation rather than evaporation.

Equation 3 can also be used to calculate the evaporation rate of isotopes of a given element, and thus the isotopic fractionation of evaporation residues as a func-tion of the amount of the element evaporated. The relationship between the amount of an element that has evaporated and the associated isotopic fractionation of the residue is of special interest because the isotopic composition provides a quantitative “fingerprint” of how much evaporation has taken place. We can use Eqn. 3 to write the the relative rate of loss by evaporation of two isotopes of i (denoted by subscripts i,1 and i,2) as

J i,2

J i,1

J i,2Pi,2

sat

J i,1Pi,1sat

mi,1

mi,2

(4a)


R2,1

J i,2

J i,1

mi,1

mi,2

, (4b)

where R2,1 is the atom ratio of isotope 2 to isotope 1 at the evaporating surface. In writing Eqn. 4b, we have assumed that isotopes mix ideally and that at the high tem-peratures of interest here equilibrium isotope fractionations between the condensed phase and the gas are negligible. Given these assumptions, the ratio of the saturation vapor pressures of the isotopically distinct gas species is the same as the isotope ratio in the condensed phase. The standard assumption until recently has been that the evaporation coefficients of isotopes of a given element are the same and therefore that the right-hand side of Eqn. 4b can be further simplified to

R2,1 mi,1 / mi,2 , but

increasingly precise measurements of the isotopic composition of evaporation resi-dues have shown that in all cases involving evaporation from crystalline and molten silicates this simplification is not warranted. As we will show in detail below, making this simplifying assumption can cause underestimates of the amount of an element evaporated by as much as a factor of two.

Equation 4b shows that the isotopic composition of the evaporation flux differs from that of the substrate by the factor

J i,2 / J i,1� � mi,1 / mi,2 , which we will call D. If

we make some further assumptions that transport process in the evaporating material are able to keep it homogeneous and that D is independent of the evolving composi-tion of the evaporating residue, then the isotopic composition of the residue will evolve by Rayleigh fractionation given by

R2,1res R2,1

0 g1D�1� �, (5)

where R2,10 is the initial isotopic composition of the condensed phase and ƒ1 is the

fraction of isotope 1 remaining in the residue. A good way of testing the validity of the assumption made in writing Eqn. 5 is to plot the experimental data as

ln R2,1

res / R2,10� � versus ln(ƒ1), which according to Eqn. 5 should fall along a straight line

with slope D–1. As shown in Section 3.1, recent experiments with high precision iso-topic analyses are very well behaved in this sense.

The relatively simple picture outlined above regarding the isotopic fractionation of evaporation residues becomes a bit more complicated as some of the simplifying assumptions are relaxed. For example, if we allow for a finite pressure of the evapo-rating species at the surface of the condensed phase (i.e., Pi / Pi

sat z 0 ) then the iso-topic fractionation factor D

J i,2 / J i,1� � mi,1 / mi,2 in Eqn. 5 should for most practical

applications be replaced by c�D� 1� (D�1)(1� Pi / Pisat ) (see Richter et al. 2002 for the

derivation of this result). The isotopic fractionation of a residue for a given amount of evaporation of the parent element will be reduced when the system becomes diffu-sion-limited to the extent that diffusion is not sufficiently fast to maintain the homo-geneity of the condensed phase. We would not expect diffusion limitations to have much effect in the case of molten CAIs or chondrules (see discussion in Richter 2004), however evaporation of solids such as forsterite will be severely diffusion-limited with the effect that isotopic fractionations will be limited to a very thin boundary layer at the surface (Wang et al. 1999).

2.2. Condensation

Equilibrium condensation calculations are discussed in more detail in another chapter

436 Davis et al.

in this volume (Petaev & Wood, this volume), so we briefly summarize recent pro-gress and discuss kinetic effects on condensation.

“Condensation calculations”, in which the thermodynamic equilibrium conden-sate assemblage is calculated as a function of temperature in a gas of fixed pressure and composition (usually solar) provide an extremely useful framework for interpret-ing bulk compositions of CAIs, chondrules, meteorites and planets. The first modern calculations for the solar system, along with a detailed description of methods, were presented by Grossman (1972). More recent calculations have explored a wider range of parameters. Wood & Hashimoto (1993) explored the effects of varying the propor-tions of four volatility components of solar material: refractory dust, carbonaceous matter, ice and hydrogen gas. They found that dust enrichment increases both the overall condensation temperatures of dust and the iron content of mafic minerals and permits melts to be in equilibrium with gas. Yoneda & Grossman (1995) explored condensation of melts in the CaO-MgO-Al2O3-SiO2 (CMAS) system and found that melts can coexist with gas at pressures as low as 10–2 atm. Earlier calculations that did not take into account the large degree of nonideal solution behavior of CMAS melts had predicted that melts would only be stable at pressures above 1 atm. Ebel & Grossman (2000) extended such calculations to chondritic compositions. Dust-enriched systems have two important differences from solar system composition: condensation temperatures are higher, so melts can be stabilized; and conditions can become oxidizing enough at high dust enrichments to allow condensation of a sig-nificant fraction of total iron into ferromagnesian minerals rather than metal (Wood & Hashimoto 1993; Ebel & Grossman 2000).

Although phase relationships among gas, solids, and liquids in equilibrium are estimated with thermodynamic calculations, condensation is a time-dependent kinetic process, which requires theory as well as kinetic data that are obtained through ex-periments. The most practical way to model condensation of CAI and chondrule melts is to apply the Hertz-Knudsen equation (Eqn. 2), which has been widely used for evaporation processes (e.g., Richter et al. 2002; Alexander 2004; Richter 2004).

J ij

cond is an extrinsic parameter that depends on the ambient gas pressure, the gas composition, and the composition of the condensed phase, whereas

J ij

evap is an intrin-sic parameter that depends only on the composition of the evaporating (condensed) phase at a given temperature. At equilibrium, condensation and evaporation fluxes must be balanced, and

J ij

cond and J ij

evap must be the same. In vacuum, under free evaporation conditions, the evaporation flux is maximized and the condensation flux is zero. It is generally assumed that

J ij

cond is constant and the same as J ij

evap determined through free evaporation experiments to meet the requirement of conditions at equi-librium (e.g., Alexander 2004; Richter 2004). This is the simplest kinetic model for condensation and evaporation, but is not necessarily correct, because the physical processes pertinent to the two parameters are different. The evaporation coefficient is the ratio of the number of evaporated atoms at a condition of interest (P, T, and gas composition) to the number of atoms impinging on a condensed phase at correspond-ing equilibrium, whereas the condensation coefficient is the ratio number of con-densed atoms at a specific condition to the number of impinging atoms on the sur-face. Thus, the two parameters are not necessarily the same, except at equilibrium.

In order to describe the condensation process as a time-dependent process, we have to know the condensation and evaporation coefficients as a function of partial


pressure of the species and gas composition. We cannot, however, obtain the two pa-rameters independently, and therefore, the net coefficient should be experimentally obtained as a function of gas pressure (composition), which is fairly difficult task to perform. Evaporation coefficients have been determined from a number of vacuum evaporation experiments, but condensation coefficients have only been measured for metallic iron.

3. Experiments

Evaporation of CAI and chondrule compositions in the laboratory have confirmed much of the theoretical understanding of evaporation processes, but have also shown the need for experimentally determined parameters in models. A good example of this is isotopic fractionation of magnesium. It is commonly assumed that the isotopic fractionation factor for magnesium is given by the square root of the masses of the magnesium isotopes, e.g., 24 / 25 (i.e., that J24Mg= J25Mg), yet well-controlled ex-periments evaporating crystalline forsterite (Mg2SiO4), liquid Mg2SiO4, melts of ini-tially chondritic composition and CAI melts consistently give fractionation factors D significantly closer to one than 24 / 25 (see below). In models relating the degree of mass loss of magnesium with isotopic fractionation, the experimentally determined fractionation factor must be used.

Much less has been accomplished in condensation experiments, because of the difficulty in achieving experimental conditions plausible for the solar nebula.

3.1. Evaporation

Quantitative evaporation experiments using solar system and solar system-like mate-rials to explore chemical fractionation were pioneered by Hashimoto (1983; 1990) and expanded to isotopic fractionation by Davis et al. (1990). The compositions that have been most extensively studied in evaporation experiments intended for applica-tion to the solar system are pure forsterite, a Type B CAI-like liquid consisting of CaO, MgO, Al2O3 and SiO2, and a liquid in which major oxides, including those of iron, are initially in solar proportions. Three major types of experiments are done: (1) “vacuum” experiments, in which a sample is usually hung from a wire loop in the center of a continuously pumped furnace with pressure <10–6 torr (e.g., Hashimoto 1990; Nagahara & Ozawa 1996; Tsuchiyama, Takahashi, & Tachibana 1998; Wang et al. 1999; Richter et al. 2002); (2) low pressure hydrogen experiments run at ~10–3 bar in a highly modified vertical tube furnace (e.g., Kuroda & Hashimoto 2002; Rich-ter et al. 2002), an evacuated vertical tube furnace (e.g., Yu et al. 2003) or resistance-heated modified vacuum furnaces (e.g., Nagahara & Ozawa 1996; Tsuchiyama et al. 1998); and (3) one atmosphere experiments run in reducing, hydrogen-rich gases in gas-mixing vertical tube furnaces (e.g., Richter et al. 2002).

Evaporation in low pressure, hydrogen-rich gas is most relevant to early solar nebula processes, but well-controlled experiments are difficult. In the apparatus used by Richter et al. (2002) and Kuroda & Hashimoto (2002), appropriate solar nebular pressures can be achieved, but temperatures are limited to 1500°C, because this is the maximum temperature capability of the apparatus. CAI compositions can be studied, because they have liquidus temperatures of ~1400°C. Chondritic compositions are more difficult, because once iron is evaporated, liquidus temperatures can easily ex-

438 Davis et al.

ceed 1500°C. Fortunately, vacuum experiments can be done to study isotopic and chemical fractionation at significantly higher temperature (Davis et al. 1998 and Davis & Hashimoto 1995 evaporated perovskite in vacuum at 2150°C) and chemical fractionation can be studied at lower temperatures in one-atmosphere gas-mixing fur-naces.

One of the most striking conclusions of Hashimoto (1990) was that evaporation of forsterite (and at higher temperatures, liquid of forsterite composition) is signifi-cantly slower than is expected from thermodynamic calculations. This difference is usually expressed as the evaporation coefficient (Eqn. 1). This conclusion seems to be a general one for silicates. In order to calculate an evaporation coefficient from a vacuum experiment, it is necessary to have a good thermodynamic model for the residue. This is straightforward for forsterite, for which thermodynamic properties are well measured. Thermodynamic models for calcium-, aluminum-rich silicate liq-uids appropriate for CAI melts are also quite good. As an example, Figure 1 shows the fit of a compositional trajectory of evaporation residues of molten MgO-CaO-SiO2-Al2O3 calculated using Eqn. 3 to data obtained from vacuum evaporation ex-periments. The data are those reported in Richter (2004) and the calculated trajectory is based on saturation vapor pressures calculated in the manner discussed in Grossman et al. (2000). The melt model is that of Berman (1983), which does an ex-cellent job in reproducing the thermodynamic properties of these highly nonideal melts. Evaporation coefficients of forsterite and CAI melts are compared in Figure 2. The data plotted were measured in vacuum experiments (1600°C and above) and in low-pressure hydrogen experiments (1500°C and below). The log of the evaporation coefficient is approximately linear with 1/T; at plausible nebular evaporation tem-peratures, 1300–1700°C, evaporation coefficients are 0.03–0.1. In other words, evaporation is only 3 to 10% of the thermodynamically expected rate. In comparing initially chondritic composition evaporation experiments of Hashimoto (1983) and Wang et al. (2001) with the most sophisticated model appropriate for chondritic sili-cate liquids, MELTS, Alexander (2002) also found evaporation coefficients signifi-cantly below 1 for Mg, Si and Fe. Hashimoto (1988), Hashimoto (1989) and Hashi-moto, Holmberg, & Wood (1989) used a vacuum furnace to perform evaporation ex-periments on a number of simple, single-component oxides and found that there was a range of evaporation coefficients, ranging from 1 to 0.03. Wang et al. (1994) showed that the evaporation coefficient for molten FeO is ~1, i.e., that there is no kinetic inhibition of evaporation; metals generally have evaporation coefficients near 1 (e.g., Tachibana, Nagahara, & Ozawa 2001).

Forsterite evaporates congruently (i.e., magnesium, silicon and oxygen all evaporate at the same rate, so that the residue does not change chemical composition) in H2 gas as well as in vacuum and that the evaporation rate of forsterite has depend-ence on H2 pressure at pressures above the equilibrium vapor pressure of forsterite (Nagahara & Ozawa 1996). The dependence of evaporation rate on hydrogen pres-sure was found to be linear with the pressure of H2 by Nagahara & Ozawa (1996) but proportional to the pressure of H by later workers (Tsuchiyama, Tachibana, & Taka-hashi 1999; Kuroda & Hashimoto 2002). The later results are what one expects from the dependence of the vapor pressure of forsterite on H in the gas. The difference may, however, be due to the nature of the forsterite charges used and/or the control of gas species in the experiments. The next step in complexity involves evaporation


studies of iron-bearing olivine, in which the residue becoming increasingly magne-sium-rich as evaporation proceeds, but the residual phase remains olivine (i.e., the fayalite component of the olivine solid solution evaporates faster than the forsterite component). The evaporation behavior of iron-bearing olivine as reported by Ozawa & Nagahara (2000) is quite complicated in that the kinetic fractionation of the Fe/Mg ratio is found to be significantly less than the values expected based on calculated equilibrium Fe/Mg distribution between Fo90-Fo99 olivine and gas (i.e., the ratio of saturation vapor pressures of Fe(g) and Mg(g) over olivine). This implies that the evaporation coefficient for evaporation of iron from olivine must be significantly lower than that of magnesium. Recall that the evaporation coefficient for evaporation of magnesium from forsterite is of the order of 0.03–0.06 (Fig. 2) while that of iron from molten FeO is ~1 (Wang et al. 1994). The clear implication is that the relative volatility of elements during kinetic evaporation depends on both saturation vapor pressures (calculable in most cases from thermodynamic data) and evaporation coef-ficients. The latter are not calculable from first principles nor can they be reliably estimated from their values in endmember silicates or oxides.

Figure 1. Chemical compositions of residues of melts of initial Type B CAI composition evaporated in vacuum at 1800°C. The solid curve is calculated from Eqn. 3 using meth-ods described in Grossman et al. (2000). The thermodynamic model for the melt (Ber-man 1983) captures the highly nonideal solution behavior of the melt quite well.

440 Davis et al.

Figure 2. Evaporation coefficients for evaporation of melts of forsterite and CAI compo-sition. Evaporation coefficients are approximately linear when plotted in this way and de-crease with decreasing temperature. Figure taken from Richter et al. (2002).

Vacuum evaporation experiments have been done on chondritic meteorites (Hashimoto, Kumazawa, & Onuma 1979; Floss et al. 1996; Floss et al. 1998) and on synthetic melts of chondritic composition (Hashimoto 1983; Wang et al. 2001). These experiments confirm that the major elements can be ordered by volatility, from volatile to refractory: iron, magnesium § silicon, calcium, and aluminum. Vacuum evaporation of REE-bearing melts leads to residues with large negative cerium anomalies (Wang et al. 2001). Evaporation of REE-bearing CAI melts in the pres-ence of hydrogen does not produce cerium anomalies because conditions remain re-ducing (Davis et al. 1999). The reason for this difference is as follows. For most REE, such as lanthanum, the evaporation reaction is H2 + La2O3 o 2LaO + H2O; for cerium, it is H2O + Ce2O3 o 2CeO2 + H2. Thus, as the oxygen fugacity is increased, the H2O/H2 ratio increases, lanthanum and most other REE become more refractory and cerium becomes more volatile; under very low pressures (as in vacuum experi-ments), cerium is significantly more volatile than the other REE.


One of the most important aspects of volatility fractionation is the relationship of elemental to isotopic fractionation. A number of evaporation experiments have been done over the past 15 years to address this issue. The first well-controlled ex-periments that maintained free evaporation conditions and carefully measured tem-perature, mass loss, and isotopic composition were those of Davis et al. (1990). In this paper, the isotopic compositions of all the elements making up forsterite were measured. In experiments above 1890°C, the melting point of forsterite, the isotopic fractionations follow a Rayleigh-like behavior, but the fractionation factors are in every case closer to one (i.e., less fractionating) than what one calculates from the inverse square root of the mass of rate-controlling gas species (Mg for magnesium, SiO for silicon, and O, O2 and SiO for oxygen). Similar deviations from inverse square root of mass behavior have been reported for: (1) vacuum evaporation of crys-talline forsterite (Wang et al. 1999); (2) vacuum evaporation of melts of initially solar composition (Wang et al. 2001); and (3) vacuum and low pressure hydrogen evapora-tion of melts of initially Type B CAI composition (Richter et al. 2002). A number of experimental difficulties have been proposed to explain the effects, but have been ruled out (Janney et al. 2004). Partial recondensation could reduce isotopic fractiona-tion, but should depend on sample size. Experiments in vacuum and low-pressure hydrogen showed no variation of fractionation factor with sample size (Richter et al. 2002; Mendybaev, Davis, & Richter 2002; Janney et al. 2004). Diffusion limited transport within the residue could also reduce isotopic fractionation, but the residues are quenched within two minutes and no chemical gradients are present in CAI resi-dues, which quench to glass. In discussing evaporation of solid SiO2, Young et al. (1998) suggested that the kinetic fractionation factor might reflect bond breaking rather than the mean velocity of the volatilizing molecules. It seems unlikely that bond breaking can explain our results given that they involve liquids, solids and dif-ferent materials with vastly different evaporation rates depending on temperature and surrounding pressure. Furthermore, some materials such as FeO do have a kinetic isotope fractionation factor equal to the inverse square root of the evaporating species (Wang et al. 1994), which would a surprising coincidence if the fractionation were controlled by the sort of bond breaking suggested by Young et al. (1998).

The recent development of high precision isotopic analyses by multicollector inductively coupled plasma mass spectrometry (MC-ICPMS) has allowed stringent tests of Rayleigh behavior of evaporation experiments and detailed investigation of mass fractionation laws. Figure 3 shows magnesium isotopic compositions of a set of molten Type B CAI-like samples (~2.5 mm in size) that were evaporated in a vacuum furnace at 1800°C (Richter 2004). Here we plot ln(R/R0) vs. –lnƒ24, where R is the 25Mg/24Mg ratio of the residue, R0 is the 25Mg/24Mg ratio of the starting material, and ƒ24 is the fraction of 24Mg remaining in the residue. The slope is 1–D, where D is the gas-solid isotopic fractionation factor for 25Mg/24Mg. The data are remarkably linear and give confidence in our understanding of the evaporation process. The develop-ment of MC-ICPMS techniques has also revealed that the isotopic fractionation fac-tor for evaporation of magnesium from CAI melts is temperature dependent (Richter et al. 2005a), with the factor becoming closer to the “ideal” inverse square root of mass behavior with increasing temperature. The new data allow extrapolation of ex-perimental data to a plausible CAI evaporation temperature of 1400°C, where the measured fractionation factor implies nearly a factor of two less magnesium loss than

442 Davis et al.

the “ideal” factor (Richter et al. 2005a). Data for evaporation of magnesium from forsterite and chondritic melts lies along the same fractionation factor vs. temperature relationship, suggesting little matrix dependence for magnesium evaporation.

Figure 3. Magnesium isotopic composition vs. fraction of 24Mg remaining for vacuum evaporation of Type B CAI composition at 1800°C in vacuum. The linear relationship in this plot shows that this experiment exactly follows Rayleigh behavior with a fixed gas-solid isotopic fractionation factor.

In contrast, the isotopic fractionation factor for silicon does seem to be matrix dependent, becoming closer to the “ideal” inverse square root of the mass of SiO value in the order forsterite, chondritic melt, CAI melt (Davis et al. 1990; Wang et al. 2001; Janney et al. 2005). There also seems to be a fundamental difference between silicate and oxide liquids, in that during evaporation of FeO, the isotopic fractiona-tion factor is equal to the inverse square root of the mass of evaporating Fe atoms, whereas in evaporation of iron from an initially chondritic silicate melt, the isotopic fractionation factor is significantly less (Dauphas et al. 2004).

Table 1 presents a summary of isotopic fractionation factors from evaporation experiments. All measured fractionation factors are less than the “ideal” values, with the exception of evaporation of FeO. The values in Table 1 are recommended for use in deducing degree of elemental fractionation from isotopic data on chondrules and CAIs.


Table 1. Isotopic mass fractionation factors for evaporation of solar system materials.

T D-1 D-1 D-1 Conditions Composition

°C Mg Si Fe

ratio 25/24 29/28 56/54

— 0.02023 0.01117 0.01802 “ideal”

1500 0.01203±0.000731 low P H2 CAI

1600 0.01243±0.000192 Vacuum CAI

1600 0.01842±0.000473 Vacuum FeO

1700 0.01308±0.000162 Vacuum CAI

1700 0.01305±0.000673 Vacuum chondrite

1800 0.01367±0.000222 0.0102±0.00044 Vacuum CAI

1800 0.01361±0.000475 0.00861±0.000195 Vacuum chondrite

1900 0.01409±0.000152 Vacuum CAI

1900 0.01535±0.000996 0.00755±0.000056 Vacuum forsterite

2000 0.01542±0.000715 Vacuum chondrite

2050 0.01573±0.000886 Vacuum forsterite 1�Richter et al. (2002); 2�Richter et al. (2005a); 3�Dauphas et al. (2004); 4�Janney et al. (2005); 5�Wang et al. (2001); 6�Davis et al. (1990).

3.2. Condensation

Condensation experiments relevant to plausible solar nebular conditions are most difficult, because: (1) it is hard to maintain a continuous supply of gas with constant composition and no isotopic fractionation; (2) it is hard to achieve the molecular and elemental composition of high temperature solar composition gas and condense mul-tielement silicates and oxides from that gas, and (3) condensation is strongly con-trolled by the design of experimental apparatus used. Limited numbers of condensa-tion experiments have been carried out so far, which are intended to produce analogs of planetary or astrophysical objects. Those are reaction experiments of gas with sili-cate melt to reproduce chondrules (e.g., Georges, Libourel, & Deloule 2000; Tis-sandier, Libourel, & Robert 2002) and reproduction of phases from multicomponent gas at low pressure simulating condensation in the solar nebula (Toppani et al. 2004). These experiments do not yield condensation coefficients, because of their experi-mental design.

The role of pressure during evaporation of material into a gas of its own vapor was studied by Inaba et al. (2001) for forsterite and Tachibana et al. (2001) for metal-lic iron. Those experiments were conducted in capsules with different lengths in or-der to vary the pressure above the sample. Pressure in individual capsules is calcu-lated assuming conductance in a tube. Evaporation rates were obtained for various pressures between vacuum and equilibrium vapor pressure. The evaporation rate of forsterite varies almost linearly with pressure from vacuum to the equilibrium vapor pressure at 1700°C, and Jcond is shown to be constant at the same value as Jevap. The evaporation rate of iron were determined at 1074–1445°C and pressures from vac-uum to equilibrium, and it shows pressure dependence at all the temperatures. Jcond is

444 Davis et al.

close to unity at a temperature close to the melting point, and becomes smaller with decreasing temperature. There appears to be some decoupling of Jevap and Jcond away from equilibrium.

Experiments to get kinetic parameters of condensation have succeeded only for metallic iron. Tatsumi et al. (2004) heated metallic iron at 1350°C to produce gas, which condensed at lower temperatures. The condensates are crystalline iron regard-less of condensation temperature, although the size of crystals varied depending on condensation temperature and duration. Jcond is obtained to be 0.6 to 0.8. It is inde-pendent of condensation temperature, although a small dependence may exist. The value is close to the evaporation coefficient of Fe in vacuum and at various Fe pres-sures at nearly the same temperature (Tachibana et al. 2001), suggesting similar val-ues of Jcond and Jevap for Fe .The experiments were carried out in a constant flux for each condensation temperature, and it is not known whether Jcond depends on pres-sure. Experiments to obtain condensation coefficients of elements for condensation of silicates and silicate melts have not yet succeeded.

4. Applications

4.1 General Rules about Elemental and Isotopic Volatility Fractionations

Elemental fractionation, such as depletion of volatile elements like potassium, iron, magnesium and silicon relative to refractory elements like aluminum and calcium, can be accompanied by isotopic mass fractionation under conditions dominated by kinetic effects. In order to achieve such fractionations in bulk, diffusion must be rapid compared to evaporation in the residue and the ambient gas pressure must be low enough to prevent significant back reaction. If these conditions are not achieved, it is possible for significant elemental fractionation to occur without significant isotopic fractionation. Detailed consideration of these effects can be found in Ozawa & Na-gahara (2000), Richter et al. (2002), Richter (2004), and Alexander (2004).

4.2. CAIs

There is surprisingly little evidence for pristine, direct condensates among CAIs, as strong textural and petrologic arguments for subsequent melt crystallization can be made for some CAIs and for most others the mineralogy is too simple for strong pet-rologic constraints and textures are equivocal. In the 1970s, the best-known CAIs were the large Type A and B CAIs in CV chondrites. Type A CAIs are dominantly melilite and spinel; Type B CAIs have these phases plus fassaite and anorthite. At the time, it was argued that most of these CAIs are condensates, because their mineral-ogy matched that from condensation calculations and they are enriched in lithophile and siderophile elements by a factor of ~20 relative to CI chondrites (Grossman 1972; Grossman 1973). It is now clear that although there may have been condensate precursors to these CAIs, the last event they experienced was one of heating and crystallization from a melt.

Careful determination of bulk chemical compositions of Type B CAIs have re-vealed that they are depleted in magnesium and perhaps silicon relative to composi-tions predicted from equilibrium condensation calculations (Grossman et al. 2000;


Simon & Grossman 2004). These CAIs also have correlated enrichments in the heavy isotopes of silicon and magnesium (Clayton, Hinton, & Davis 1988), very similar to what has been measured in laboratory produced evaporation residues (Davis et al. 1990; Wang et al. 2001). Both the elemental abundances and isotopic compositions of CAIs can be understood by evaporation of equilibrium condensates from a gas of solar composition (Grossman et al. 2000) and the correlated elemental and isotopic fractionation effects have been reproduced in laboratory evaporation of CAI melts under plausible solar nebular conditions (Richter et al. 2002). Type B CAIs have ig-neous textures indicating that they were once reheated to several hundred °C above their condensation temperatures for plausible nebular pressures and remained par-tially molten (T|1400°C) for at least several hours and then cooled at a few degrees per hour (Stolper & Paque 1986). The duration of this high temperature event is such that significant evaporative loss of magnesium, silicon and oxygen is to be expected given the evaporation kinetics of these elements from Type B CAI-like liquids in a low-pressure hydrogen-dominated gas (Richter et al. 2002). A plausible source of the reheating is the passage of a shock wave, and Richter et al. (2005b) show that the temperature and pressure history of a CAI subject to the Desch & Connolly (2002) canonical shock will fractionate the elemental and isotopic composition of a reason-able precursor (i.e., a condensate from a solar composition gas) so as to produce a very typical Type B CAI. An alternative model for formation of Type A and B CAIs involves single stage closed system evaporation of cold CI chondrite-like precursors under conditions of enhanced dust/gas ratios at distances of 2–3 AU (Alexander 2004). Under these conditions, partial back-reaction reequilibrates isotopic composi-tions while permitting elemental fractionation. However, evaporation under enhanced dust/gas ratios leads to more oxidizing conditions, where cerium is more volatile than other REE. While a few unusual CAIs have negative cerium anomalies (Davis et al. 1982; Ireland et al. 1990), most do not, indicating that most CAIs evaporated under highly reducing conditions. Furthermore, a significant fraction of titanium in fassaite in CAIs is trivalent (Dowty & Clarke 1973; Simon, Grossman, & Davis 1991) indi-cating oxygen fugacities typical of a gas of solar composition (Beckett 1986). A third astrophysical setting for CAI formation is close to the Sun, where Shu and colleagues have suggested that CAIs were melted near the X-point in an X-wind model (Shu et al. 1997, 2001). The X-wind model has not yet been tested in this detail for CAIs be-cause it has not yet produced time-temperature-pressure trajectories that can be put into evaporation-condensation models and compared with CAI compositions.

There is other evidence for evaporation having played a role in CAI formation, in addition to the common enhancement in the heavy isotopes of magnesium and sili-con in CAIs discussed above. Melilite in CAIs is a solid solution between gehlenite (Ca2Al2SiO7) and åkermanite (Ca2MgSi2O7). Crystallization experiments on melts of CAI composition show that the first melilite to crystallize contains about 20 mole% åkermanite (Åk20) and melilite near the outside of CAIs typically shows a broad area of melilite of about this composition. However, within 100–200 µm of the outer edge of CAIs, much more gehlenitic melilite (Åk0–10) is commonly found. An example is shown in Figure 4. Such gehlenitic melilite is very difficult to explain by simple melt crystallization of melts of CAI bulk composition, but may be the result of evapora-tion. Davis, Mendybaev, & Richter (2004) reported that subsolidus evaporation of

446 Davis et al.

melilite in the presence of hydrogen causes growth of gehlenitic melilite. CAIs are

Figure 4. A compositional profile from the outside (0 µm) to the inside of Allende Type B CAI USNM5241. Note that inward of ~200 µm, the Åk content of melilite rises smoothly, interrupted by a couple of positive excursions. The excursions may represent an interruption in the cooling history or a boundary between two melilite crystals. The smooth increase from 200 to 650 µm is the behavior expected for the first melilite to crystallize. Outside of 200 µm, the Åk content drops precipitously, likely the result of subsolidus evaporation of melilite. In some areas of this and other CAIs in CV chon-drites, the Åk content drops to below 2 mole %.

commonly rimmed by a series of thin layers, consisting, from inside to out, of spinel plus perovskite, melilite, calcic pyroxene zoned from titanium-rich to titanium-poor, and forsterite (Wark & Lovering 1977). The spinel-perovskite layer sometimes con-tains hibonite, and the spinel often pseudomorphs hibonite, so the layer may have consisted of hibonite with or without perovskite (Davis, MacPherson, & Hinton 1986). The origin of Wark-Lovering rims has been debated since their discovery, but it now seems possible that the spinel-hibonite-perovskite layer formed as a result of evaporation, as Davis, Mendybaev, & Richter (2004) found that subsolidus evapora-tion of melilite in the presence of hydrogen can cause growth of hibonite. Relatively slow growth of this layer under near-equilibrium conditions might explain the lack of isotopic fractionation observed in Wark-Lovering rims compared to interiors of


CAIs. Further work is clearly needed on experimental tests of Wark-Lovering rim formation. There is also stronger isotopic and textural evidence for evaporation hav-ing played a major role in the formation of the unusual Vigarano CAI 1623-5. This CAI shows isotopic and petrologic evidence for evaporation (Davis et al., 1991) and recent ion microprobe measurements of oxygen and magnesium isotopes suggest that the CAI was evaporating as it crystallized (Davis, McKeegan, & MacPherson 2000; McKeegan et al. 2005).

4.3. Chondrules

Chondrules exhibit a wide range of bulk compositions, most notably in their alkali and FeO contents, but also in their SiO2 and MgO contents. These variations are con-sistent with evaporative loss (e.g., Jones 1990; Sears, Huang, & Benoit 1996). Evi-dence for condensation of FeO- and SiO2-rich material that probably evaporated dur-ing chondrule formation is particularly well preserved in chondrule rims in Bishunpur (LL3.1) (Alexander 1995). Chondrules also show clear evidence for open system be-havior during crystallization. Libourel, Krot, & Tissandier (2005) demonstrated that chondrule glasses show negative correlations between SiO2 and Al2O3 as well as be-tween SiO2 and CaO. These correlations are inconsistent with closed-system crystal-lization of chondrule bulk compositions and require addition of SiO2 from an external source during crystallization. There is also evidence for evaporation of iron metal (Kong, Ebihara, & Palme 1999; Connolly, Huss, & Wasserburg 2001) and SiO2 (Krot et al. 2003) from CR chondrite chondrules and recondensation of them in chondrule rims and interchondrule matrix. Zonation of alkalis and other elements in Semarkona (LL3.0) chondrules have been interpreted as being due to reentry either during chon-drule cooling (Matsunami et al. 1993; Nagahara et al. 1999; Libourel et al. 2003), or during aqueous alteration on the Semarkona parent body (Grossman et al. 2002; Alexander & Grossman 2005). The presence of an outer zone of low-calcium pyrox-ene phenocrysts in many otherwise olivine-dominated type I chondrules has been interpreted as due to recondensation of silica during chondrule cooling (Tissandier et al. 2002).

It has been suggested that type IA chondrules could have formed from precur-sors with type IIA-like compositions (e.g., Sears et al. 1996). If this occurred via evaporation under Rayleigh conditions, then from their average compositions (Jones & Scott 1989; Jones 1990) the expected isotopic fractionations in potassium, iron, silicon and magnesium in type IA chondrules would be about 11, 9, 3 and 2 (‰ amu-1), respectively. Of course, the total range in elemental compositions seen in in-dividual chondrules are much larger, so the total range of isotopic fractionations pre-dicted would be much greater. Yet there is remarkably little isotopic fractionation observed in chondrules (Table 2), and what fractionations have been found do not vary in a simple way with chondrule composition.

The absence of significant systematic isotopic fractionations in chondrules can be explained in one of two ways: either chondrules were open (Sears et al. 1996) but evaporation occurred in such a way that elemental fractionation was not accompanied by isotopic fractionation (Alexander et al. 2000; Galy et al. 2000), or chondrules re-mained closed during formation and inherited their compositions from their precur-sors (Grossman & Wasson 1982, 1983). With the recent evaporation experiments and

448 Davis et al.

kinetic modeling, it is now possible to begin to quantitatively address this longstand-ing debate.

Table 2. Isotopic mass fractionation effects in chondrules.

Isot. Fract.

(‰ amu–1) Source

K

Allende (CV3) <0.35 Humayun & Clayton (1995)

Bishunpur (LL3.1) <1-2a Alexander et al. (2000)

Semarkona (LL3.0) <1-2a Alexander & Grossman (2005)

Fe

Chainpur (LL3.4) <1 Alexander & Wang (2001)

Chainpur (LL3.4) 0.2 Zhu et al. (2001)

Chainpur (LL3.4) 0.2 Mullane et al. (2003a)

Tieschitz (H3.4) 0.15 Kehm et al. (2003)

Allende (CV3) 0.6 Zhu et al. (2001)

Allende (CV3) 1.1 Mullane et al. (2003b)

Si

Chainpur (LL3.4) 0.4 Clayton et al. (1991)

Dhajala (H3.8) 0.5 Clayton et al. (1991)

Mg

Tieschitz (H 3.4) 1 Nguyen, Alexander, & Carlson (2000)

Allende (CV3) 1 Galy et al. (2000)

Allende (CV3) 1.5 b Young et al. (2002) aLarger fractionations were measured, but a lack consistency between isotopic compo-sition and K depletion suggests that these may be instrumental artifacts. bSome of this variation is due to secondary alteration.

The canonical conditions for chondrule formation suggest that they were rapidly

heated to near-liquidus temperatures (porphyritic chondrules) and superliquidus tem-peratures (barred and excentroradial chondrules), and then cooled at rates of 10-1000 K h–1 (Hewins et al. this volume). Liquidus temperatures vary with composition, but are typically ~1700–2100 K (Hewins et al. this volume). The largest depletions in alkalis, iron and even silicon and magnesium, relative to aluminum, are found in type IA chondrules, which have the highest liquidus temperatures.

Under these conditions, vacuum evaporation rates for potassium suggest that chondrules will be open (Yu et al. 2003). From a series of experiments, Cohen, Hewins, & Alexander (2004) estimate that at 1853 K and PH2

§10–5 bars it would take ~3 hours to produce an FeO-poor type IA chondrule from a FeO-rich CI-like precur-sor, and at PH2

§10–3 bars it might take only about 20 minutes. These timescales are of the order predicted from the estimated cooling rates and by shock heating models (Iida et al. 2001; Ciesla & Hood 2002; Desch & Connolly 2002; Miura, Nakamoto, & Susa 2002).


Based on petrologic evidence, it has been suggested that chondrules formed by multiple very short heating events (Wasson, this volume). There is debate about this interpretation of the petrologic evidence (Hewins et al. this volume). However, the cosmic spherules (Section 4.3) suggest that flash heating and cooling alone is not suf-ficient to prevent isotopic fractionation. If chondrules were heated on shorter time-scales and to lower temperatures than cosmic spherules, isotopic fractionations in an individual event may be reduced, but it is likely that the net effect of multiple events would be significant isotopic fractionation. In our theoretical understanding of evapo-ration, we cannot distinguish between a single longer event and a series of shorter events. Under a particular set of conditions, both will yield the same result.

If we accept the canonical chondrule formation conditions, experiments suggest that chondrules would have been open for the alkalis (Yu et al. 2003) and probably for other elements (e.g., Cohen, Hewins, & Alexander 2004). The absence of signifi-cant systematic variations in chondrule isotopic compositions requires that isotopic fractionation be suppressed while allowing elemental fractionation. Isotopic frac-tionation could be suppressed by high PH2

(Section 2.1) or by enhanced dust/gas ra-tios.

For a millimeter-sized object, PH2 would have to exceed ~10–2 bars for free

evaporation to be suppressed sufficiently to begin affecting isotopic fractionations (Richter et al. 2002). Galy et al. (2000) have suggested that a PH2

of up to one bar may be needed to explain the small magnesium isotopic fractionations seen in chon-drules with a large range of MgO contents. Estimated midplane pressures will vary depending on the disk model and phase of evolution (Bell et al. 1997). The highest pressures will exist near the Sun (~0.1 AU). At high mass accretion rates, midplane temperatures near the Sun may be too high to form chondrules (>2000 K). At low mass accretion rates, the pressure near the Sun is <10–2 bars (Bell et al. 1997). Shock waves could enhance pressures but ambient temperatures near the Sun are >1000 K even at very low accretion rates, making it difficult to explain the high abundance in chondrules of volatile elements such as sulfur.

If high PH2 is an unlikely explanation for the lack of isotopic fractionations of

chondrules during melting, they must have equilibrated with the evaporated gas (Alexander et al. 2000). If this is the case, chondrule melts must be stable under rea-sonable nebular conditions, and there must be enough time for equilibration between the chondrules and gas to take place. Simple models suggest that both requirements may be satisfied if PH2

= 10-4-10-3 bars and dust/gas ratios are ~100-1000 times solar (Ebel & Grossman 2000; Alexander 2004), although it is not clear how such condi-tions can be achieved. However, the kinetic models of Alexander (2004) were iso-thermal and did not include crystallization so their results should be treated with cau-tion. Gas-melt equilibration would have continued during chondrule cooling. Ther-modynamic models suggest that this would have involved reentry of many elements (Ebel & Grossman 2000). The temperature at which an element ceased equilibrating will have depended on chondrule cooling rate, its diffusivity in the chondrule melt and its vapor pressure in the nebula. There is evidence that the rapidly diffusing alka-lis continued to equilibrate with the gas until crystallization of clinopyroxene (~1200–1400 K), presumably just before final solidification of the chondrules (Jones 1994; Libourel, Krot, & Tissandier 2003; Alexander & Grossman 2005). Ozawa & Nagahara (2001) estimate that suppression of isotopic fractionation and gas-

450 Davis et al.

chondrule equilibration of K would have occurred provided that cooling rates were below ~300 K h–1 and dust was enriched relative to chondrules.

4.3. Micrometeorites

The precursors of most silicate spherules were roughly chondritic in composi-tion, and most were probably of asteroidal origin (Dermott et al. 2002). Typically asteroidal particles have atmospheric entry velocities close to the escape velocity (~11 km s–1). In the course of approximately 10 seconds as it decelerates in the upper atmosphere, a typical spherule is heated to temperatures that approach or exceed its liquidus, and then cools down to ambient temperatures (Love & Brownlee 1991). Temperatures may only exceed 1000°C for a few seconds. Peak heating occurs be-tween altitudes of 100 and 80 km (Love & Brownlee 1991), where ambient pressures range from 10–7 to 10–5 bars (U.S. standard atmosphere 1976), respectively. Thus, aspects of spherule formation resemble the rapid heating particles experience as they are overtaken by a shock wave in nebular shock models of chondrule formation (Iida et al. 2001; Ciesla & Hood 2002; Desch & Connolly 2002; Miura et al. 2002). For instance, in their modeling Desch & Connolly (2002) estimate shock speeds of ~6 km s–1 and initial ambient pressures of ~10–5 bars. Many spherules even exhibit textures that resemble chondrules (e.g., porphyritic textures with relict grains and barred oli-vine textures), although others have cryptocrystalline textures not found in chon-drules of similar composition.

A realistic model of atmospheric entry heating has yet to be developed. Love & Brownlee (1991) estimated peak temperatures for asteroidal particles of 1500–1600°C and as 1700–1800°C for high velocity cometary particles. Using a more real-istic evaporation model calibrated against evaporation experiments, Alexander & Love (2001) estimated substantially higher peak temperatures, but even this model does not capture the potential complexity of entry heating (Toppani et al. 2001).

While spherule precursors may have had roughly chondritic compositions, spherules have a range of compositions that strongly suggest significant evaporation. Isotopic measurements confirm this and indicate a very similar behavior to the evaporation experiments despite the very different conditions. There is significant potassium loss in even the least heated spherules (Taylor et al. 2005). As in vacuum evaporation experiments (Yu et al. 2003), potassium isotopic fractionation associated with evaporation from the spherules follows the Rayleigh fractionation law with a fractionation factor equal to the square-root of the potassium isotope masses (Fig. 5). Large iron isotope mass fractionation effects are found in some silicate spherules, but they are less than expected for Rayleigh fractionation with the isotopic fractionation factor equal to the square root of the iron masses (Alexander et al. 2002; Taylor et al. 2005). This is probably because a lot of iron may be reduced and expelled as metal blebs. Magnesium and silicon show isotopic fractionations of up to ~12‰ amu–1 for magnesium and ~8‰ amu–1 for silicon in so-called CAT (calcium-, aluminum-, tita-nium-rich) spherules (Alexander et al. 2002; unpublished). However, difficulties in making appropriate standards for the ion microprobe measurements means that there is some uncertainty in these values, particularly for magnesium. Estimates of the de-grees of loss based on (Mg,Si)/Al ratios suggests that the evaporation behavior for


these two elements approximated Rayleigh-like behavior (Fig. 6 shows data for sili-con isotopes).

Figure 5. Potassium isotopic composition of cosmic silicate spherules, which evaporated on atmospheric entry. The line is not a fit through the data. Rather it is the predicted tra-jectory for Rayleigh evaporation of material with an initial (K/Al)CM ratio of 1, where the gas-solid fractionation factor is given by the inverse square-root of the masses of the po-tassium isotopes.

In conclusion, flash heating of silicate and metal on the order of seconds does not suppress evaporation and associated isotopic fractionation. Chondrules are up to a factor of 5 larger than the measured spherules (200-400 Pm across compared to up to 1 mm across). Depending on diffusion rates, it is possible that isotopic fractionations were suppressed in larger chondrules. Charges of several mm across in vacuum evaporation experiments show similar evaporation behavior to spherules. Thus, diffu-sion is only likely to influence isotopic fractionation if evaporation rates were en-hanced by high PH2

during chondrule formation.

452 Davis et al.

Figure 6. Silicon isotopic composition of cosmic silicate spherules. The line is the pre-dicted trajectory for Rayleigh evaporation of material with an initial (Si/Al)CM ratio of 1, where the gas-solid fractionation factor is given by the inverse square-root of the ratio of masses of 28Si16O and 30Si16O. The line provides a reasonable description of the data, but is not as convincing as the case for potassium.

Acknowledgments. The work was supported by the National Aeronautics and Space Administration through grants to Davis, Alexander and Richter.

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