42nd Lunar and Planetary Science Conference (2011)
2367.pdf
A MODEL FOR TRACE ELEMENT PARTITIONING IN METALLIC SYSTEMS CONTAINING
MULTIPLE LIGHT ELEMENTS. J. A. Van Orman1, L. A. Hayden2, 1Dept. of Geological Sciences, Case Western Reserve University, Cleveland, OH 44106, 2Dept. of Geological Sciences, University of Michigan, Ann Arbor
MI 48109.
Introduction: The partitioning of elements among
solid and liquid iron alloys plays a key role in the
chemical evolution of planetary and asteroidal cores.
Experimental studies performed over the last several
decades have established that non-metallic “light” alloying components such as S, C and P exert a primary
control on trace element partition coefficients1-6. For
example, in sulfur-bearing systems the solidmetal/liquid-metal partition coefficients of platinumgroup elements increase by several orders of magnitude as the sulfur content in the liquid increases from
zero toward the eutectic composition7,8. On the other
hand, the solid/liquid partition coefficients for elements including Cu, Cr, Pb and V decrease strongly as
the sulfur content in the liquid increases9. For the
platinum group elements there is evidently a repulsive
interaction with sulfur in the liquid, while in the latter
case the interaction with sulfur is attractive. Trace
element partition coefficients are also found to vary
significantly with the C or P content of the liquid
metal5,6.
Jones and Malvin3 showed that the partition coefficient for several trace elements in the Fe-Ni-S and
Fe-Ni-P systems could be represented in terms of the
liquid composition alone, without taking into account
the temperature or solid properties, according to:
Ν
Ν
Feï(Ni)ïS
Feï(Ni)ïS
model
Feï(Ni)ïP
FeïC
5
4
3
Ν
Ν
Ν
6
(1)
In this equation, xN is the molar fraction of the nonmetallic element (S or P) in the liquid metal, β is a
constant that represents the interaction between the
trace element of interest and the non-metallic element
in the liquid, n is a stoichiometry factor that depends
on the speciation of the non-metal in the liquid, α is an
empirical constant with a value close to unity, and Do
is the solid/liquid partition coefficient at infinite dilution (i.e. when no non-metallic elements are present in
the liquid). A similar expression was proposed for iron
alloy systems containing multiple light elements, with
the parameter β a weighted average of the values in
the simple systems, and was found to be broadly consistent with the available partitioning data for Ge and
Ni in the Fe-Ni-S-P system3.
Chabot and Jones4 presented a similar model that
also assumes the partition coefficient is a power-law
function of the liquid metal composition. As in the
Jones and Malvin model, the liquid metal is assumed
to contain non-metallic species such as FeS, Fe3C and
Fe3P, with the remainder being metal. The partition
coefficient is parameterized as:
(2)
Where (Fe domains) represents the molar fraction of
metallic species in the liquid. The primary difference
with the Jones and Malvin model is that each nonmetallic species is assumed to have an identical influence on trace element partitioning. Chabot and Jones
found their parameterization to be in good agreement
with partitioning data for the Fe-(Ni)-S system and in
reasonable agreement with the sparse data for the Fe(Ni)-C and Fe-(Ni)-P systems that existed at the time.
However, more recent experiments on carbon-5 and
phosphorus-bearing6 systems have shown that many
trace elements do not behave in the way the Chabot
and Jones model predicts. Tungsten, for example, is
strongly repelled by sulfur in the liquid, but experiences a strong attractive interaction with carbon and a
weak attractive interaction with phosphorus in the liquid (Fig. 1). The W partitioning data for each system
can be fit separately to equation (2), but in each case
the value of β is different. In this case, and several
others, there is no way to parameterize the full data set
in terms of the Chabot and Jones model.
ln(D)
ln(D) = ln(Do) + β ln(1-α nxN).
ln(D) = ln(Do) - βln(Fe domains)
2
1
0
ï1
ï2
0.2
a
0.4
0.6
Fe domains
0.8
1
Figure 1: Solid-liquid partition coefficients for W plotted versus the molar fraction of metallic species in the
liquid. Data sources: Fe-(Ni)-S2,8,12, Fe-(Ni)-P6, Fe-C5.
Furthermore, we have found that recent data on
trace element partitioning in the Fe-S-C system10,11
cannot be parameterized by the Jones and Malvin or
Chabot and Jones models, particularly for elements
like W and Mo. There are two major issues in applying these parameterizations to systems with multiple
non-metallic elements. First, the models do not describe well the behavior of elements like W and Mo
that are attracted to one light element (carbon) while
42nd Lunar and Planetary Science Conference (2011)
Model: Our new parameterization for trace element partitioning in multi-component iron alloy systems is based on a metallurgical formalism in which
the activity coefficient for the trace element of interest
is expanded in a Taylor series about the infinitely dilute (i.e. pure Fe-Ni metal) reference state13. For the
Fe-S-C system, neglecting terms of order greater than
two, the activity coefficient for a trace element is expressed as:
2
ln γ = ln γ  + ε FeS x FeS + ρ FeS x FeS
+ ε Fe 3C x Fe 3C
2
+ρ Fe 3C x Fe 3C + ρ FeS −Fe 3C x FeS x Fe 3C
€
where x denote the molar fractions of FeS and Fe3C
species, ε and ρ are first- and second-order interaction
coefficients and γo is the activity coefficient in the pure
Fe-Ni alloy. The partitioning of a trace element between two phases depends on the ratio of the activity
coefficients in each phase. Thus, in terms of Eqn. 3,
ten interaction coefficients must be defined to determine a trace element’s partition coefficient between
two phases in the ternary Fe-S-C system. However,
we have found that good fits to the available trace element partitioning data for between solid/liquid, liquid/liquid and even Fe3C/liquid in the Fe-S-C and Fe(Ni)-S-P systems are obtained by assuming that the
interaction coefficients are the same in each phase
(solid metal, cohenite, and each liquid). Under this
assumption the partition coefficient between any two
phases is expressed (for the Fe-S-C system) as:
ln D = ln D  + ε FeS ( Δx FeS ) + ρ FeS ( Δx FeS )
(
)
(
+ε Fe 3C Δx Fe 3C + ρ Fe 3C Δx Fe 3C
(
+ρ FeS −Fe 3C ( Δx FeS ) Δx Fe 3C
€
(3)
)
)
2
2
(4)
where Δx refers to the difference in the molar fraction
of FeS or Fe3C in the two phases that the trace element
is partitioning between, and Do refers to the partition
coefficient between two phases that have the same
chemical composition (e.g. between solid and liquid in
the pure Fe-Ni system). Systems containing phosphorus are included by adding interaction terms for Fe3P to
Eqn. 4. Figure 2 compares the experimental partitioning data for W, one of the elements that is fit least well
by the Jones and Malvin and Chabot and Jones models,
to modeling results based on Eqn. 4, where the interac-
tion coefficients were obtained by multiple linear regression of the experimental data. Experimental data
from many different systems, with partition coefficients ranging over several orders of magnitude, are
included on Fig. 2, and all are fit quite well by the
model. Similarly good fits are obtained for all other
trace elements (>20) for which experimental data are
available.
8
6
4
Feï(Ni)ïS
FeïCïS solid/liquid
FeïCïS liquid/liquid
FeïC solidïmetal/liquid
FeïC cohenite/liquid
Feï(Ni)ïSïP
Feï(Ni)ïP
ln(D)
being repelled by another (sulfur). Second, they do not
consider interactions with light elements that are dissolved in the solid phase. In particular, carbon dissolved in solid iron appears to have a significant influence on trace element partition coefficients in the FeS-C system, comparable to its influence in the liquid10,11.
2367.pdf
2
W
0
ï2
ï2
0
2
ln(Dmodel)
4
6
8
Figure 2: Comparison of experimental and model data
for W partitioning in iron alloy systems. Similarly
good fits to the model are obtained for >20 other trace
elements.
Discussion: An important advantage of the model
presented here is that it can be used to estimate partition coefficients in regions of composition space that
have not been studied experimentally. In particular,
we have found that the cross terms (e.g. the final term
in Eqn. 4) are generally small, and that the partition
coefficients in the Fe-S-C and Fe-S-P systems are predicted reasonably well based on interaction parameters
determined from the simple binary systems Fe-S, Fe-C
and Fe-P.
References: [1] Willis J., Goldstein J.I. (1982) J.
Geophys. Res. 87, A435-A445. [2] Jones J.H., Drake
M.J. (1983) GCA 47, 1199-1209. [3] Jones J.H.,
Malvin D.J. (1990) Metall. Mater. Trans. 21B, 697706. [4] Chabot N.L., Jones J.H. (2003) Met. Planet.
Sci. 38, 1425-1436. [5] Chabot N.L. et al. (2006) GCA
70, 1322-1335. [6] Corrigan C.M. et al. (2009) GCA
73, 2674-2691. [7] Fleet M.E. et al. (1999) GCA 63,
2611-2622. [8] Chabot N.L. et al. (2003) Met. Planet.
Sci. 38, 181-196. [9] Chabot N.L. et al. (2009) Met.
Planet. Sci. 44, 505-519. [10] Hayden L.A. et al.
(2010) 41st LPSC #1520. [11] Hayden L.A. et al.
(2011) GCA in review. [12] Liu M. and Fleet M.E.
(2001) GCA 65, 671-682. [13] Lupis C.H.P. (2003)
Chemical Thermodynamics of Materials, NorthHolland, 581 pp.