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A dendritic solidification model to explain Ge-Ni variations in iron meteorite chemical groups
Geochimica 0 Pergamon
et Cosmochimicu Acta Vol. 46, pp. 259 to 268 Press Ltd. 1982. Printed in U.S.A.
A dendritic solidification model to explain Ge-Ni variations in iron meteorite chemical groups C. NARAYAN and J. I. GOLDSTEIN Department
of Metallurgy
and Materials
Engineering,
Lehigh
University,
Bethlehem,
PA 18015
(Received April 20, 1981; accepted in revised form October 5, 1981) Abstract-Segregation during solidification is responsible for the secondary fractionation of trace elements in iron meteorite chemical groups. This study examines the consequences of dendritic segregation on the Ge-Ni fractionation in iron meteorite chemical groups. Solidification experiments and computer simulations of the dendritic solidification process indicate that the effect of P on the partitioning behavior of Ge and the effect of solid state diffusion on segregation are both important in understanding the observed Ge-Ni correlations. The Ge-Ni concentration trends predicted by the dendritic solidification model agree well with the observed variations.
Fig. 1, are non-linear in some of the chemical groups. In addition, there are marked differences in the slopes of the log Ge vs. log Ni plots for various chemical groups. Group IVA has a changing positive slope while group IIIAB exhibits a slope reversal and group IAB has a negative slope. These three groups contain nearly 70% of all metallic meteorites. In the light of the discrepancies between the predicted and observed Ge concentration trends, the assumption of plane front solidification needs to be examined. Recent work on thermal modeling of parent bodies and experimental solidification studies of Fe-Ni alloys (Goldstein et al., 1979; Narayan and Goldstein, 1981) indicate that dendritic solidification is a possible freezing mode in meteorite parent bodies. This paper discusses the consequences of dendritic solidification of parent body cores. A model of the freezing process which yields the variation of trace element concentration with Ni content is developed using the results of solidification experiments.
INTRODUCTION
IRON METEORITESare classified by means of their structure and chemistry. The chemical grouping based on the concentrations of Ge, Ga and Ir and their correlations with Ni content (Goldberg et al., 1951; Lovering et al., 1957; Wasson, 1967, 1969, 1970; Wasson and Kimberlin, 1967; Wasson and Schaudy, 1971, Schaudy et al., 1972; Scott et al., 1973; Scott and Wasson, 1975; Kracher et al., 1980) can be used to understand the fractionation behavior of the parent meteorite body. The variation of Ge and Ni concentrations in iron meteorites is shown in Fig. 1. Although the Ge concentrations vary by over a factor of 14,000 (Wasson, 1967), the Ge and Ni concentrations of the iron meteorites cluster into specific com~sitional groups. A primary fractionation event is believed to be responsible for the formation of the groups. Theories based on nebular processes such as fractional condensation and selective accretion have been developed to explain this clustering (Wasson and Wai, 1976; Anders, 1964; Kelly and Larimer, 1977; Sears, 1978, 1979). These primary fractionation models predict the formation of meteorite parent bodies composed of Fe-Ni cores surrounded by silicate shells. During cooling and solidification the trace elements in the metallic core segregate. This segregation process is responsible for the observed chemical fractionation within meteorite groups (Fig. 1). The extent of segregation, and the resulting trace element concentration trends, depend on the mode of solidification. Current theories attempt to explain the chemical fractionation by assuming plane front solidification in the Fe-Ni core (Scott, 1972). A plane front solidification model predicts a linear variation of the log of the trace element concentration X with the log of the Ni concentration so long as the solid/ liquid partition coefficients remain constant during solidification. Each chemical group should have the same linear variation of log X versus log Ni. The observed variations of log Ge vs. log Ni, shown in
BACKGROUND
Dendritic solidification of the cores of parent bodies will result in segregation of trace elements. To study the segregation pattern, ternary partition coefficients f&$ of trace elements in Fe-Ni alloys are necessary. The ternary equilibrium partition coefficient, Kg of an element X can be defined as I$ = c&fc;
(1)
where C$ is the concentration of X in the solid and Cf is the concentration of X in the liquid in equilibrium with the solid. The fractionation of elements between dendrite cores and edges, assuming solid state diffusion is insignificant, is characterized by the Scheil equation: cl; = C
(2)
where Ct is the bulk concentration of element X, Kt is the equilibrium ternary partition coefficient of X and Cs is the concentration of X in the solid form259
260
I
r
c‘. NARAYAN
AND J. 1. GOLDSTEIN
IIII
-l
100
F
‘O
‘i
a
= 0
.-._ I WA IV0
0.1 Q
7
Flc,. 1. Chemical
IO
1 4
1
20
%Ni
grouping of iron meteorites vs. log Ni plot. (Scott. 1979)
ments are present in very small amounts and do not affect the soiidification behavior of Fe-N{ alloys. However, elements such as P, S and C can have ;I significant effect on the solidification temperatures of Fe-Ni alloys. The binary Fe-P phase diagram (Hawkins, 1973) indicates that even though pure iron is solid below 153O”C, an alloy with as little ah 0.2 wt% P retains some liquid to below 1450°C:‘. while -2 wt% P retains some liquid an alloy containing to below 1150°C. Most meteorite groups cuntain I-” in varying amounts. Although chemical group IVh has only 0.09 wt% (Willis, 1980), group 1I 1AB me, teorites have an average P content of 0.26 wt’X# (Buchwald, 1975) with several meteorites containing over 0.5% wt% P and group IAB meteorites contain significant amounts of P, C and S. Because meteorite magmas have enough P to alter the melting point trt Fe-Ni-Ge alloys an experimental technique was developed in order to measure @ as ;1 function <,f temperature and P content.
on a log Ge
ing at the solid-liquid interface when a fraction ,f; ot the dendrite has solidified. From equation (2), during the first stage of freezing (f.* = 0), Ki:= Ct/Cfwhere Cz is the concentration of the first solid to freeze. If the dendrite core composition, Cf, is not altered by solid state diffusion, the equilibrium K$ values can be estimated by measuring the core and bulk compositions of dendritically solidified alloys. If solid state diffusion is important, the measured partition coefficient (Kt)values can be corrected for diffusion using the method of Brody and Flemings (1966) to yield equilibrium K$ values. Narayan and Goldstein (198 1) have experimentally measured partition coefficients of ternary additions to Fe-Ni alloys and equilibrium K$ values were obtained for Ni, Au, Ge, Pt and P. In addition, they demonstrated that diffusion in the solid during solidification is significant for Ge and P whose measured partition coefficient values differ by >lO% from the equilibrium K$ values. The experimentally determined @ value in FeNi (Narayan and Goldstein, 198 1) is 0.58 and does not vary with Ni content. The use of this @ value in either a planar front or dendritic solidification model will yield a positive slope of log Ge vs. log Ni for any iron meteorite chemical group. Solid state diffusion effects in the dendritic model will yield a positive non-linear slope of log Ge vs. log Ni for any meteorite group. The measured w value cannot however be used to explain the Ge-Ni chemical groups (Fig. 1) which contain negative slopes or both positive and negative slopes. A varying log Ge-log Ni slope can be explained if f@ changes with Ni content (Wai et al., 1978). A change in I@ is possible if the temperature range for solidification of Fe-Ni was influenced by some other component in the Fe-Ni-Ge melt. Most ele-
EXPERIMENTAL
PROCEDURE
In order to measure the effect of P on pi”. alloys ot l:e,, Ni-P-Ge were held at different temperatures in the twophase solid + liquid field. The alloys were equilibrated for 2 to 4 hours and quenched in water to preserve the composition of the two phases in equilibrium. The electron microprobe was used to measure the composition of the quenched phases. The ratio of the composition of the solid to that of the liquid was used to calculate the equilibrium f@, Kg and Kr'values. (a) Choice of alloy compositions: The Fe-Ni-P-Ge alloys were induction melted from pure elements. Ni concentrations were chosen to resemble meteoritic Ni levels. The t+e.. Ni-P ternary isotherms (Doan and Goldstein, 1970) indicate that with an increase in temperature the two phase y t liquid field moves to lower Ni contents. Although the data are available only up to 1100°C the trend indicates that alloys with 9 wt% Ni and >I.5 wt% P will remain in they + liquid field from 1 1OO’C to the liquidus temperature near 1450°C. On this basis a Ni content of approximately 9 wt% was chosen for the alloys. Germanium levels in me teorites range from a few rg/g to >400 rg/g and this would, therefore, be an ideal range of Ge concentrations for the experimental alloys. However, reliable quantitative information from the electron microprobe demands Ge levels 2 0.5 wt% (Goldstein and Yakowitz, 1975). Most alloys. therefore, contained between 0.5 and 1.0 wt% Ge. The bulk P content of the alloy is not critical as long as the alloy remains in they + liquid field at the temperature of interest. For reliable chemical data, a liquid volume fraction greater than -0.2 was desirable. To maintain at least 20% liquid at the equilibration temperature. P levels between 2 and 6 wt% were chosen. (b) The equilibrium experiment: The bulk alloy of a chosen composition was placed in an alumina crucible 2.5 cm long and 1.0 cm in diameter (Coors Porcelain, Colorado). The crucible was then lowered into a vertical tube furnace (Lemont Scientific) in a platinum basket. A schematic drawing of the set-up is shown in Fig. 2. A steady Row of Ar was maintained through the furnace during the experiment to prevent oxidation of the alloy. A Pt-Pt-13% Rh thermocouple was used to monitor the temperature inside the furnace adjacent to the suspended crucible. The temperature was raised to 145O’C for 5 minutes to melt the alloy and then lowered to the equilibration temperature The equilibration temperatures ranged from 1099“C to
SOLIDIFICATION
OF IRON
261
METEORITES
THERMOCOUPLE PLATINUM SUSPENSION WIRE -
i )_
ARGON OUT
otHEATING
ELEMENT
FURNACE TUBE c_
ARGON IN
(-<; f-1: (-QUENCH
VERTICAL
TUBE
TANK
FURNACE
FIG. 2. A schematic drawing of the vertical used for the equilibrium experiments.
tube furnace
137O’C. The alloy was held at the equilibrium temperature for 2 to 4 hours so that the coexisting y and liquid phases would reach equilibrium and was then quenched in water. The quenched sample was sectioned normal to its circular cross-section, mounted in lucite and polished. The surface was etched with 2% nital to reveal the microstructure. Fig. 3 shows a typical microstructure where the large grains are y at the equilibration temperature. The regions of dendritic structure between the y grains were the regions of liquid at the equilibration temperature. The liquid phase solidified
FIG. 4. Position of a typical probe trace across the y phase at the equilibration temperature. S: solid, L: modified liquid, Arrow: indicates the microprobe trace. The alloy had a nominal composition of Fe-14% Ni-2% P-l% Ge and was equilibrated at 1370°C. Bar = 100 em.
as fine dendrites during the quench. Samples that had more than 0.2 volume fraction liquid were used for chemical analyses. (c) Microanalysis of the equilibrated samples: The samples were repolished with 6 zrn and 1 pm diamond paste and etched lightly to help locate areas of interest for microprobe analysis. Quantitative analysis of the solid phase involved several random point analyses on different grains. Homogeneity of the grains was checked by taking a composition trace across a grain. Fig. 4 shows a typical grain that was checked for homogeneity and Fig. 5 shows the com~sitional homogeneity of that grain. A small increase in the P concentration near the edge of the grain is caused by diffusion from the P rich region during the quench. Homogeneity of the grains and the uniform composition of the different grains confirmed equilibrium between the
1 t
04
-
t GRAIN EDGE +
0 FIG. 3. A modified solid (S) + liquid (L) structure obtained on quenching an equilibrated alloy. The alloy had a nominal composition of Fe-lo% Ni-2% P-l% Ge and was equilibrated at 142O’C. Bar = 100 sm.
I
1
20
40
I 60
, 60
I
I 100
I20
140
pm FIG. 5. Com~sitional homogeneity in the solid phase as shown by the electron microprobe trace across a prior y grain shown in Fig. 4.
262
AND J. I. GOLDSTEIN
c‘. NARAYAN
TABU i Typical
data
obtained
from an equilibrium
Fe-9% Ni-2%
P-11.4% Ct: and was equili.brared
-B of analysis
%Ni (wt) In solid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.37 8.25 8.21 8.61 8.46 8.34 a.47 8.26 8.09 8.16 8.08 8.38 8.20 7.90 7.80
Average
t
8.24
in
(wt)
%P
liquid
%P (wt) in liquid
1.015
8.89
+0.004
kO.41
+ 0.03
1099’)C.
P
-
8.04 8.28 9.42 8.82 8.79 9.05 9.16 8.81 8.54 9.10 10.39 8.72 8.27 8.89 9.11
1 .Ol 1.02 1.01 i.01 2.02 I.02 1.02 1.00 1.02 1.02 1.01 1.02 1.02 1.02 0.99
9.86
= 0.84
-_I
_--.5.85 10.01 9.85 10.33 10.18 9.59 9.97 9.56 10.02 9.76 9.82 9.50 9.94 9.35 10.14
%Ge (wt) in solid _... ._._._-_ l.Oi I. 03
I.09 I *i:?l I. 05 i.09 1. 09
I .:I? ! *iI4 i.08 1.08 1.11 1 .il 1 .li, 1 Y04 1.08
-
L
_I.-
K, = 0.114
of
--...-__--
(wt)
in solid
-+0.19
at
-
~I___
%Ni
---
The a1 lay had a !::)mina i :ompo,. i tion
experiment.
-+ 0.005
i .
phases. Composition of the dendritically sohdlhed hquid phase was evaluated through several area scans (40 pm x 50 wrn) and defocused beam analyses (50 pm diameter beam). Small pools of liquid were avoided because their composition could be altered during the quench by the rejection of P by the surrounding grains. The compositions of the solid and the liquid were used to calculate F$. KE and Kt’. RESULTS
The equilibrium experiments were conducted at 1099”C, 1192”C, 1265”C, I3 18°C and i37O”C. Table 1 shows the data obtained from a t-e-Ni-Cie-P sample held at 1099°C for 3 hours. Analyses from 15 regions of former y and liquid phases are given.
The small spread in the compositlon of the soi~ti indicates equilibration at the heat treatment temper, ature. The greater spread in the composition ~11‘the liquid is partially due to the selection of liquid poolh of different sizes. Even within a large pool trf liquid 3 small range of compositions can he t’xpcclt’d tfu~, to sampling differences during area scans ;i~rtl dcfocused beam analyses. The k$’ values cai~latcd from the equilibrium experiments are given ii! ‘I’ahle 2. The functional dependence of @ on the uquillhration temperature is shown in Fig. O. \ leasr squares line drawn through the data points >i&is the following relationship A<;’ ~ ~-3.25 X 10 ’ I : 5.,34 0 ~-
: :>
where T is the temperature in “C. Table I 4s~) i151t the solubility limit of P in the solid at the Itvc cquilibration temperatures.
-1
DISCUSSION (a) Quality oj‘experimentul data. The error in I!ic measured equilibrium partition coefficient Glrise~ from the errors in the measurements of the cumpositions of the solid and the dendriticaily solidified liquid phases. At least 15 random measurements were made on each phase to calculate the range of homogeneity for Ni. P and Ge. The level of homogeneity for a given (1 - a) confidence level ir given hy (Goldstein and Yakowitr, 1975)
FIG. 6. Measured bration temperature.
values
of ti;C a!, a function
of equih-
SOLIDIFICATION
263
OF IRON METEORITES TABLE 2
Dependence
of
Ge KO on the
phosphorus
in 1.02 0.79 0.62 0.43 0.20
1099Oc 1192w 1265 ‘C
i3ia”c 137oOc 15ooOc
and
Ge (wt%) in solid
P (wt%)
T(‘C)
content
solid _+ 0.004 2 0.02 _+ 0.01 _+ 0.02 _+ 0.006 0.00
the
temperature.
in
(wt%) liquid _+ 0.05 _+ 0.04 _+ 0.04 _+ 0.04 _+ 0.03
Ge
1.08
_+ 0.04
1.14 1.10
2 0.02 _+ 0.04
0.78 0.82
_+ 0.03 _+ 0.01
0.67 0.82 0.89 0.81 1.15
solidified
ternary
KGe
0
1.61 _+ 0.14 1.39 _+ 0.07 1.24 _+ 0.07 0.96 _+ 0.06 0.71 _+ 0.02 0.58(*)
I This
data
point
is
taken
from
a dendritically
where WI_, is the range of homogeneity, C is the true concentration of the element in weight fraction, n is the number of measurements, N is the average number of x-ray counts accumulated during each analysis, S, is the standard deviation associated with the total counts, tA-7 is the student t value for (n - 1) degrees of freedom. The term kW,_,/C represents the composition spread around C in relative percent. Table 3 shows the homogeneity data for an alloy equilibrated at 1099°C for 3 hours. The equilibrium partition coefficient Kf is the ratio of the concentration of X in the solid to that in the liquid. If +Rs is the composition spread in the solid phase and fRL that in the liquid phase, both in relative percent, then the range of Kt values is + (Ri + Ri)“’ in relative percent. Table 4 lists KFi, G and @ values for the different temperatures. All error calculations have been made at a 99% confidence level. (b) Effect of Ge content on @. Germanium contents in meteorites range from a few pg/g to >400 pg/g. Reliable quantitative x-ray data from the equilibrium experiments required Ge levels up to 1 wt%. However, Ge concentrations up to 1 wt% do not have any measurable effect on the liquidus and solidus lines of Fe-Ni. Since P influences the solidus and
alloy
Fe-Ni-Ge.
liquidus compositions drastically, its effect on @ can be assumed independent of the bulk Ge content provided that the Ge level is
time
(6)
TABLE 3 Level
of
homogeneity
for
an
Confidence
Element Nickel in Nickel in Phosphorus Phosphorus Germanium Germanium
Solid Liquid in Solid in Liquid in Solid in Liquid
n
+ n-l
15 15 15 15 15 15
2.977 2.977 2.977 2.977 2.977 2.977
alloy
held
Leve 1:
at
1099’C
for
99%.
C&W 0.03 0.03 0.005 0.06 0.05 0.09
3 hours.
a.24 9.86 1.02 8.89 1.08 0.67
X KO
1-U
_+ 0.19 _+ 0.23 2 0.004 + 0.41 _+ 0.04 + 0.05
0.84 0.115 1.61
2 0.03 _+ 0.005 + 0.13
264
C. NARAYAN
AND J. 1. GOLDSTEIN
Table 5 lists the primary dendrite arm spacing (d) and the corresponding solidification time ($) for an Fe-lo% Ni alloy for cooling rates ranging from O.O2”C/sec to l”C/sec. The data have been ab,stracted from Figure 4-3 and Appendix B of Barone rt al., (1964). The ratio of d to the square root of 8, is constant to within 10% with an average value of 26 pm/G. This value together with an estimate for cooling rate in meteoritic parent body cores can be used to estimate primary dendrite arm spacing in parent body cores. If a cooling rate of 1“C per million years (Goldstein and Short, 1967) is assumed for the parent body cores the solidification time is 5 million years and the primary dendrite width would be 325 meters. To get another independent estimate 01‘ the dendrite size in parent bodies Fe-lo% Ni alloys were directionally solidified in the laboratory to yield dendrites aligned with the growth direction. The experiment was carried out for three different solidification times and the results are shown in Table 6. The ratio d/fifis again constant to within 10% with an average value of 59 @m/e. Extrapolation of this data to meteoritic solidification times of 5 million years yields a primary dendrite about 750 meters wide. This estimate is about twice the previous estimate. The difference may be due to the different experimental technique employed in that the dendrite spacing is very sensitive to several experimental parameters (Barone ef al. 1964). Both sets of data. however, indicate that primary dendrites in parent bodies could be typically between 100 and 1000 meters wide. (d) Solid state diffusion in dendrites Dendritic solidification of an alloy leads to the segregation of
the solute element between the dendrite core alrd the dendrite edge. Chemical fractionation of the solute sets up concentration gradients within the dendrite which results in the diffusion of the solute down the concentration gradient. The extent to which solid state diffusion can reduce compositional inhomo geneities depends on the diffusivity (D) of the elcment, the distance over which the solute atom has to diffuse (x) and the time available for diffusion (I). If the diffusivity of the solute elemem is indcpendent of composition or varies only sligbtlq in the composition range being considered, then I he con. centration change due to diffusion is a single valued function of the variable x/21/‘D7 (Reed-Hill, lY7.3). As an example, if two similar alloys are cooled a! two different rates to produce dendrites of sizes 1, and x2 and if t, and t2 are the corresponding timeh available for diffusion in these dendrites, then the changes in the core compositions of these dcndrlteh due to diffusion will be the same if
Work on measurement of partition coefficients from dendritically solidified alloys (Narayan and Goldstein, 1981) indicates that diffusion effects are considerable in 100 pm dendrites in the 500 seconds required for the alloy to cool from if;OO”C tc~ 1000°C. If a cooling rate of I “C per million years (Goldstein and Short, 1967) is assumed for parent body cores then the time for cooling from 1500°C MI 1000°C is 500 million years and equation (8 j prcdiets that diffusion will be considerable in a dendrite that measures 560 meters across. Diffusion corrections are important for elements like Ge and P whose diffusivities in Fe-Ni are higher than 10 ” ~~m’/sec at 1300°C (Narayan and Goldstein, 198 1I. In the previous section primary dendrites in parent body cores were estimated to be typically -500 nteters across. Diffusion corrections are therefore importarlt in modeling segregation of Ge and P in parenr hod&. (e) Simulation of theJractionution o/ m/nor rir.ments in iron meteorite chemical groups. A primal, fractionation model is believed to be responsible for the formation of meteorite parent bodies with I c-Ni cores of uniform compositions corresponding to the average compositions of the chemical groups. When the homogeneous molten Fe-Ni cores solidify tither
SOLIDIFICATION
OF IRON METEORITES
dendritically or with a plane front the attendant segregation together with solid state diffusion effects determine the final trace element concentration distribution within the core. The extent of segregation and diffusion will depend on the freezing mode. During later stages of cooling the segregated asteroids are broken up by collisions. Since, in the event of dendritic solidification, the dendrites could be typically 500 meters across the fragmentation process can result in a number of pieces each several meters across coming from a single dendrite. Fig. 7 is a schematic representation of a possible fragmentation pattern yielding meteorites of a chemical group. Although the figure restricts itself to one primary dendrite, the model can be extended to a parent body where all the primary dendrites upon fragmentation, contribute members of a single chemical group of meteorites. Brody and Flemings (1966) developed a numerical plate mode1 to calculate the segregation profile of a solute element across a dendrite. They characterized the segregation profile with a volume element extending from the dendrite core to the dendrite edge. Fig. 8 is a schematic representation showing the primary dendrites and the volume element chosen for the calculations. The volume element has an infinitesimal thickness parallel to the dendrite growth direction and is divided into a number of layers along the length of the element in the transverse (X) direction. At the start of solidification all the layers are molten (X = 0). With the passage of time the layers solidify successively until all the layers are frozen at the end of solidification (X = L). At any intermediate time, t, each layer solid or liquid is assigned an average composition. The composition of the solid forming at the solid-liquid interface is given
265
b
p$HETEORITES
FROM A
CHEMICAL 0%
IY
f
GROUP
u
i DENDRITE EDGE
DENDRITE CORE
FIG. 7. A schematic drawing showing meteorites from a chemical group can be obtained from different parts of a dendrite.
teorite at a certain distance from the core. The simulated log X vs. log Ni plots can then be compared to the log X vs. log Ni plots developed from observed meteorite compositions. The shape of the simulated
s;a& SOLID 1 LIQUID
I I LIQUID l
-I-,
i
by C; =
K$-Cf
(9)
where Kt is the partition coefficient of element X, Cf is the concentration of the liquid in equilibrium with the solid of concentration C$ forming at the interface. The model assumes complete mixing of the liquid. Therefore throughout the solidification process the composition of all the molten layers is the same. After each stage of solidification the effect of solid state diffusion is calculated in the frozen layers. After complete freezing, diffusion calculations are continued until the temperature reaches 1000°C when the diffusion effects become insignificant. The details of the plate model and the diffusion calculations are discussed by Narayan and Goldstein (1981). For a ternary Fe-Ni-X alloy the solidification and diffusion model cited above will yield the segregation profile of both Ni and the ternary element, X, across the dendrite. The two profiles can be combined on a log X vs. log Ni plot where each point corresponds to a fixed distance from the dendrite core. Each point on this plot can represent the composition of a me-
DISTANCE,
X-
x =0
(DENDRITE
X * Xi
(LIQUID -SOLID
R
CORE)
SOLID
A I
INTERFArE)
+I I LIQUID
L-J
X=L
FIG. 8. The dendrite dendritic
segregation.
(MIDPOINT BETWEEN DENDRITES)
TWO
plate model used to characterize (Brody and Flemings, 1966)
266
C. NARAYAN
plot will depend i)
Equilibrium x,
ii) iii) iv) v)
on the following partition
AND
parameters:
coefficient
of element
K;
Equilibrium partition coefficient of nickel, K:’ Diffusivity of element X in Fe-Ni alloys Diffusivity of nickel in Fe-Ni alloys Starting bulk composition.
Log Ge vs. log Ni plots were developed using the model. The effect of diffusion and the functional dependence of w on the temperature, see equation (3), were both incorporated into the model. The bulk P content and solid state diffusion effects were both important in determining the tinal shape of the simulated plot. Fig. 9 shows curves for two different P levels. The curve marked low P is for an alloy with only -0.05 wt% P and @ is not noticeably changed due to P. This is evident from the straight line generated by the model without diffusion effects. The diffusion effects, however, alter this linear relationship resulting in a line with a decreasing positive slope much like the trend seen in group IVA meteorites. The second curve marked high P has 0.5 wt% P and the effect of P on ?$ is evident by the line changing its slope even before diffusion is considered. Solid state diffusion further modifies this curve to resemble the trend in group IIIAB meteorites. The
A: AFTER
DIFFUSION
B: BEFtRE
DlFFUSlON
HIGH
1 7
B 1 8
P
I
1
I
9
IO
II
NICKEL (wt.%) FIG. 9. Simulation of the general shape of Group IVA with a low P alloy and of Group lIIAB with a high P alloy.
J. 1. GOLDSTEIN
(+) signs indicate the bulk Ge and Ni concentratmns of the two alloys. Having simulated the general trends ill groups IIIAB and IVA an attempt was made to match calculated and measured Ge-Ni variations. The Cie-Nl plot was calculated using the following t’~i1uc:,.
i)
ii)
iii) iv)
Diffusivity
of Ni -= exp[ I. 15 i 0.~:. I k+i ‘%,j
et al., 1965) where C,, is the Ni COIK~~~IT~~~K~I~ Diffusivity of Ge in Fe-Ni -0.492 exp(-61,86O/RT) (Nara>.u-1 :rnd Goldstein, 198 1) Kt’ = 0.87 (Narayan and Goldstein. IO8 i : @ = A function of temperature. rqu;~riun (3).
The bulk compositions were chosen so that the calculated shapes matched the measured Gc-Ni trends. A bulk composition of 8.25% Ni. 0.?5? f” and 38 ppm Ge yielded a reasonable match f;,t group IIIAB while a composition of 8.4% Ni, O.Oj’z,. P and 0. I2 ppm Ge was suited for group IVA. Fig. i 0 shows the calculated and observed trends for the diffusivities, k. values and assumed bulk cornpositrons. The slope reversal that is predicted by the model for group IIIAB meteorites is due to the changing @. As Kri is relatively insensitive to P content (me ‘Table 4) and is always 1. A high P concentration in the bulk alloy causes @ to exceed 1.O very cariy m the freezing process. @ value!, greater than 1.O will result in a negative slope for the simulated Ge-Ni trends. Groups IAB, IIAB and IIICD exhibit such negative slopes as seen in Fig. I, In additior!, i :~uI c‘ should have an effect similar to Y on ?hl; partitioning behavior of Ge since small amounts of these elements also decrease the melting point of t-e-hi alloys. (f) Applicability of the dam to planur ,qrr.m’tA model. The log Ge vs. log Ni plots generated hq :i plane front model and a dendrite model are similar. if diffusion effects are ignored, because the segrc, gation of trace elements during plane front growth and during dendritic growth is characterized by the Scheil equation (equation 2). However, during dendritic growth, chemical inhomogeneities develop over relatively small distances making solid state diffusion considerations important (Narayan and Goldstein. 198 1). Fig. 9 shows the log Ge c’J’.log Ni plot simulated by the dendrite model for a low P Fr-Ni-PGe alloy containing 0.05 wt% P. ‘The low P levei does not influence the @ and the log Ge vs. log Ni trend, before diffusion, is linear and is the same as the trend predicted by the plane front model. However; when diffusion effects are considered the trend hccomcs non-linear and yields a changing positive slope that resembles the observed log Ge KS. log Ni xtriation
SOLIDIFICATION
-
100
SIMULATED OBSERVED
GROUP GROUP
IO f
!k 3
3 8
cooling to 1000°C can experience a fragmentation process. It is possible that the different fragments get trapped in a larger parent body at different depths from the surface. Such an incorporation of smaller bodies in a bigger body has been discussed (Scott, 1979). The exact break up and incorporation sequence is, however, unclear. The fragments buried at different depths will experience different cooling rates when the temperature drops to the Widmanstgtten precipitation range. Such a solidi~cation, fragmentation, incorporation and cooling sequence is consistent with the core model and also allows for meteorites of a given chemical group to have different cooling rates. CONCLUSIONS
I.0
Y
0.i
7
8
9
IO
II
WT. % NICKEL FIG. 10. Matching observed
267
OF IRON METEORITES
data
the calculated Ge-Ni trends with the for meteorites of Groups IIIAB and IVA.
in group IVA (Fig. 1). Fig. 9 also shows a log Ge vs. log Ni plot for a high P (0.5 wt%) Fe-Ni-Ge-P alloy. The curve before diffusion shows a slope reversal and would be similar to the trend predicted by a plane front growth model. Diffusion effects in the dendritic model only modify the shape. For an element like Ir whose diffusivity in Fe-Ni is very low at the solidification temperatures, the diffusion effects are very small (Narayan, 1980). The plane front model and the dendritic model would yield the same range of Ir concentration. For a fast diffusing species like P the dendritic model predicts excessive diffusion effects. The P concentration within a dendrite varies by only a factor 2 which is smaller than the P range seen in group IIIAB. (gf Implications ofthe core model on cooling rate studies. A range of cooling rates observed in a group (Goldstein and Short, 1967; Randich and Goldstein, 1978) appears to contradict the core model for parent bodies. However, all cooling rate investigations are based on the width of the kamacite platelets in the Widmanstatten precipitate. Therefore the cooling rates deduced are valid only in the temperature range 300°C to 700°C where kamacite precipitates in a taenite matrix. The core model on the other hand, refers to the solidification of a molten Fe-Ni core and takes place in the temperature range 1500°C to 1000°C. The parent body after solidification and
(1) Solidification experiments indicate that the effect of P on the partitioning behavior of Ge in FeNi melts is significant in understanding the measured Ge-Ni variations in iron meteorite chemical groups. (2) Computer simulations of the dendritic solidification process indicate that solid state diffusion is a significant factor in the development of chemical fractionation in iron meteorite chemical groups. (3) The Ge-Ni concentration trends predicted by the dendritic solidification process may explain the types of log Ni log Ge curves found for meteorite groups in nature. (4) The dendritic solidification model, including effects of solid state diffusion, should be considered as a viable alternative to the more well known planarfront model for solidification of metallic cores of asteroidal bodies, Acknowle&ments-The authors gratefully acknowledge the financial support provided by NASA through Grant NGR 39-007-043. The authors also wish to thank J. T. Wasson of IJCLA and D. Uhlmann of MIT for their reviews which were very helpful in improving the manuscript,
REFERENCES Anders E. (1964) Origin, age and composition of meteorites. Space Sri. Rev. 3, 583-714. Barone R. V., Brody H. D. and Flemings M. C. (1964) Investigatjon of Solidification of High-Strength Steel Castings. Interim Report, Tech. Repf. #AMRA CR64 04/3, Dept. of Army Project #lA02440A i IO. Brady H. D. and Flemings M. C. (1966) Solute Redistribution in Dendritic Solidification. Trans. AlME 236, 615-624. Buchwald V. F. (I 975) Handbook of Iron Meteorites. Vol. 1, University of California Press. Doan A. S., Jr. and Goldstein J. I. (1970) The ternary phase diagram, Fe-Ni-P. Met. Trans. 1, 1759-1767. Flemings M. C., Poirier D. R., Barone R. V. and Brody H. D. (1970) Microsegregation in Iron-base Alloys. J. Iron and Steel Inst. 208, 321-381. Goldberg E., Uchiyama A. and Brown H. (1951) The distribution of nickel, cobalt, gallium, palladium and gold in iron meteorites. Geochim. Cosmochim. Acta. 2, l-25. Goldstein J. I., Hanneman R. E. and Ogilvie R. E. ( 1965) Diffusion in the Fe-Ni system at 1 atm and 40 K bar pressure. Trans. TMS-AIME 233, 8 12-820.
268
C. NARAYAN
AND J. 1. GOLDSTEIN
Goldstein J. I., Narayan C. and Soroka W. ( 1979) Sohdification of metallic cores in meteoritic parent bodies. ~eteoriti~s 14, 403. Goldstein J. I. and Short J. M. ( t 967) The iron meteorites, their thermal history and parent bodies. Geochim. Cosmochim. Acto 31, 1733- 1770. Goldstein J. I. and Yakowitz H. (eds.) (1975) Practical Scanning Electron Microscqy. Plenum Press. New York. Hawkins D. T. (1973) Mei& ~oadb#k. American Society for Metals. Vol. 8, p. 304. Kelly R. W. and Larimer J. W. (1977) Chemical fraction in meteorites-VII1 iron meteorites and the cosmochemical history of the metal phase. Geochim. Cosmochim. j4cta. 41, 93-I 1 I. Kracher A., Willis J. and Wasson J. T. (1980) Chemical classification of iron meteorites- IX. A new group (IIF), revision of IAB and IIICD and data on 57 additional irons. Geochim. Cosmochim. Acta 44, 773-787. Lovering J. F., Nichiporuk W., Chodos A. and Brown H. (1957) The distribution of gallium, germanium, cobalt, chromium and copper in iron and stony-iron meteorites in relation to nickel content and structure. Geochim. Cosmochim. Acta 11, 263-278. Narayan C., M.S. Thesis, Lehigh University. 1980. Narayan C. and GoIdstein J. I. (1981) Experimental determination of ternary partition coefficients in Fe-N&X alloys. Met. Trans. A., submitted for publication. Randich E. and Goldstein J. I. (1978) Coding rates of hexabedrites. Geochim. Cosmochim. ilcro. 42, 14 I - 150. Reed-Hi11 R. E. (I 973) Physical Merallurgy Principles. D. Van Nostrand Company, New York. Schaudy R., Wasson J. T. and Buchwaid V. F. (1972) The chemical classification of iron meteorites---Vl. A reinvestigation of irons with Ge concentrations lower than 1 ppm. Icarus 17, 174-192. Scott E. R. D. (1972) Chemical fractionation in iron meteorites and its interpretation. Geochim. Cosmuchim. Acta. 36, 120% 1236.
Scott E. R. D,. Wasson J. T. and Buchwald V. F. (1973) The chemical classification of iron meteorites-~-VII. A reinvestigation of irons with Ge concentrations between
25 and 80 ppm. Geochim. 1983.
Cosmochim.
Acts
37, 1957-
Scott E. R. D. and Wasson 3. T, (197.5) ~lassi~cation and properties of iron meteorites. Rev. Geophw and Span Physics
13(4), 527-546.
Scott E. R. D. (1979) Origin of Iron Meteorites. In As., teroids (T. Gehrels and M. S. Matthews eds.) 892-925. Sears D. W. (1978) The nature and origin of meteorites. Monograph on Astronomicai Subjects: 5, Oxford Unr. versity Press, New York. Sears D. W. (1979) Did iron meteorites form tn rhe asteroid belt? Evidence from thermodynamic models. Icurus fspecial asteroid issue). Wai C. M., Wasson J. T., Willis, J. and Kracher A. ( 1978) Nebular condensation of moderately volatile elements, their abundances in iron meteorites and the quantization of Ge and Ga abundances. Lunar Science IX, I 193- 1195. Wasson J. T. (1967) The chemical classification of iron meteorites--I. A study of iron meteorites with low concentrations of gallium and gaermanium. Geuchim. litv mochim.
Acta 31, 161- 180.
Wasson J. T. (1969) The chemical classificatron of Iron meteorites--III. Hexahedrites and other irons with germanium concentrations between 80 and 200 ppm. GE(I’ chim. Cosmochim.
Acta 33, 859-876.
Wasson J. T. (1970), The chemical classification of rron meteorites-iv. irons with germanium concentrations greater than 190 ppm and other meteorites associated with group I. Icarus 12, 407-423. Wasson J. T. and Kimberlin J. ( 1967) The chemical ciassification of iron meteorites--II. Irons and pallasites with germanium concentrations between 8 and IO0 ppm. C;eo chim. Casmo~him.
Acta 31, 20652093.
Wasson _I. T. and Schaudy R. (1971) The chetmcai classification of iron meteorites--V. Groups IIIC and IHD and other irons with germanium concentrations between I and 25 ppm. Icarus 14, 59-70. Wasson J. T. and Wai C. M. (1976) Explanations for the low Ga and Ge concentrations in some iron meteorites. Norure 261, 114-l 16. Willis .I. (~980) The bulk ~om~sition of iron meteorite parent bodies. Ph.D. Thesis, University of California. Los Angeles, 208 pp.
et Cosmochimicu Acta Vol. 46, pp. 259 to 268 Press Ltd. 1982. Printed in U.S.A.
A dendritic solidification model to explain Ge-Ni variations in iron meteorite chemical groups C. NARAYAN and J. I. GOLDSTEIN Department
of Metallurgy
and Materials
Engineering,
Lehigh
University,
Bethlehem,
PA 18015
(Received April 20, 1981; accepted in revised form October 5, 1981) Abstract-Segregation during solidification is responsible for the secondary fractionation of trace elements in iron meteorite chemical groups. This study examines the consequences of dendritic segregation on the Ge-Ni fractionation in iron meteorite chemical groups. Solidification experiments and computer simulations of the dendritic solidification process indicate that the effect of P on the partitioning behavior of Ge and the effect of solid state diffusion on segregation are both important in understanding the observed Ge-Ni correlations. The Ge-Ni concentration trends predicted by the dendritic solidification model agree well with the observed variations.
Fig. 1, are non-linear in some of the chemical groups. In addition, there are marked differences in the slopes of the log Ge vs. log Ni plots for various chemical groups. Group IVA has a changing positive slope while group IIIAB exhibits a slope reversal and group IAB has a negative slope. These three groups contain nearly 70% of all metallic meteorites. In the light of the discrepancies between the predicted and observed Ge concentration trends, the assumption of plane front solidification needs to be examined. Recent work on thermal modeling of parent bodies and experimental solidification studies of Fe-Ni alloys (Goldstein et al., 1979; Narayan and Goldstein, 1981) indicate that dendritic solidification is a possible freezing mode in meteorite parent bodies. This paper discusses the consequences of dendritic solidification of parent body cores. A model of the freezing process which yields the variation of trace element concentration with Ni content is developed using the results of solidification experiments.
INTRODUCTION
IRON METEORITESare classified by means of their structure and chemistry. The chemical grouping based on the concentrations of Ge, Ga and Ir and their correlations with Ni content (Goldberg et al., 1951; Lovering et al., 1957; Wasson, 1967, 1969, 1970; Wasson and Kimberlin, 1967; Wasson and Schaudy, 1971, Schaudy et al., 1972; Scott et al., 1973; Scott and Wasson, 1975; Kracher et al., 1980) can be used to understand the fractionation behavior of the parent meteorite body. The variation of Ge and Ni concentrations in iron meteorites is shown in Fig. 1. Although the Ge concentrations vary by over a factor of 14,000 (Wasson, 1967), the Ge and Ni concentrations of the iron meteorites cluster into specific com~sitional groups. A primary fractionation event is believed to be responsible for the formation of the groups. Theories based on nebular processes such as fractional condensation and selective accretion have been developed to explain this clustering (Wasson and Wai, 1976; Anders, 1964; Kelly and Larimer, 1977; Sears, 1978, 1979). These primary fractionation models predict the formation of meteorite parent bodies composed of Fe-Ni cores surrounded by silicate shells. During cooling and solidification the trace elements in the metallic core segregate. This segregation process is responsible for the observed chemical fractionation within meteorite groups (Fig. 1). The extent of segregation, and the resulting trace element concentration trends, depend on the mode of solidification. Current theories attempt to explain the chemical fractionation by assuming plane front solidification in the Fe-Ni core (Scott, 1972). A plane front solidification model predicts a linear variation of the log of the trace element concentration X with the log of the Ni concentration so long as the solid/ liquid partition coefficients remain constant during solidification. Each chemical group should have the same linear variation of log X versus log Ni. The observed variations of log Ge vs. log Ni, shown in
BACKGROUND
Dendritic solidification of the cores of parent bodies will result in segregation of trace elements. To study the segregation pattern, ternary partition coefficients f&$ of trace elements in Fe-Ni alloys are necessary. The ternary equilibrium partition coefficient, Kg of an element X can be defined as I$ = c&fc;
(1)
where C$ is the concentration of X in the solid and Cf is the concentration of X in the liquid in equilibrium with the solid. The fractionation of elements between dendrite cores and edges, assuming solid state diffusion is insignificant, is characterized by the Scheil equation: cl; = C
(2)
where Ct is the bulk concentration of element X, Kt is the equilibrium ternary partition coefficient of X and Cs is the concentration of X in the solid form259
260
I
r
c‘. NARAYAN
AND J. 1. GOLDSTEIN
IIII
-l
100
F
‘O
‘i
a
= 0
.-._ I WA IV0
0.1 Q
7
Flc,. 1. Chemical
IO
1 4
1
20
%Ni
grouping of iron meteorites vs. log Ni plot. (Scott. 1979)
ments are present in very small amounts and do not affect the soiidification behavior of Fe-N{ alloys. However, elements such as P, S and C can have ;I significant effect on the solidification temperatures of Fe-Ni alloys. The binary Fe-P phase diagram (Hawkins, 1973) indicates that even though pure iron is solid below 153O”C, an alloy with as little ah 0.2 wt% P retains some liquid to below 1450°C:‘. while -2 wt% P retains some liquid an alloy containing to below 1150°C. Most meteorite groups cuntain I-” in varying amounts. Although chemical group IVh has only 0.09 wt% (Willis, 1980), group 1I 1AB me, teorites have an average P content of 0.26 wt’X# (Buchwald, 1975) with several meteorites containing over 0.5% wt% P and group IAB meteorites contain significant amounts of P, C and S. Because meteorite magmas have enough P to alter the melting point trt Fe-Ni-Ge alloys an experimental technique was developed in order to measure @ as ;1 function <,f temperature and P content.
on a log Ge
ing at the solid-liquid interface when a fraction ,f; ot the dendrite has solidified. From equation (2), during the first stage of freezing (f.* = 0), Ki:= Ct/Cfwhere Cz is the concentration of the first solid to freeze. If the dendrite core composition, Cf, is not altered by solid state diffusion, the equilibrium K$ values can be estimated by measuring the core and bulk compositions of dendritically solidified alloys. If solid state diffusion is important, the measured partition coefficient (Kt)values can be corrected for diffusion using the method of Brody and Flemings (1966) to yield equilibrium K$ values. Narayan and Goldstein (198 1) have experimentally measured partition coefficients of ternary additions to Fe-Ni alloys and equilibrium K$ values were obtained for Ni, Au, Ge, Pt and P. In addition, they demonstrated that diffusion in the solid during solidification is significant for Ge and P whose measured partition coefficient values differ by >lO% from the equilibrium K$ values. The experimentally determined @ value in FeNi (Narayan and Goldstein, 198 1) is 0.58 and does not vary with Ni content. The use of this @ value in either a planar front or dendritic solidification model will yield a positive slope of log Ge vs. log Ni for any iron meteorite chemical group. Solid state diffusion effects in the dendritic model will yield a positive non-linear slope of log Ge vs. log Ni for any meteorite group. The measured w value cannot however be used to explain the Ge-Ni chemical groups (Fig. 1) which contain negative slopes or both positive and negative slopes. A varying log Ge-log Ni slope can be explained if f@ changes with Ni content (Wai et al., 1978). A change in I@ is possible if the temperature range for solidification of Fe-Ni was influenced by some other component in the Fe-Ni-Ge melt. Most ele-
EXPERIMENTAL
PROCEDURE
In order to measure the effect of P on pi”. alloys ot l:e,, Ni-P-Ge were held at different temperatures in the twophase solid + liquid field. The alloys were equilibrated for 2 to 4 hours and quenched in water to preserve the composition of the two phases in equilibrium. The electron microprobe was used to measure the composition of the quenched phases. The ratio of the composition of the solid to that of the liquid was used to calculate the equilibrium f@, Kg and Kr'values. (a) Choice of alloy compositions: The Fe-Ni-P-Ge alloys were induction melted from pure elements. Ni concentrations were chosen to resemble meteoritic Ni levels. The t+e.. Ni-P ternary isotherms (Doan and Goldstein, 1970) indicate that with an increase in temperature the two phase y t liquid field moves to lower Ni contents. Although the data are available only up to 1100°C the trend indicates that alloys with 9 wt% Ni and >I.5 wt% P will remain in they + liquid field from 1 1OO’C to the liquidus temperature near 1450°C. On this basis a Ni content of approximately 9 wt% was chosen for the alloys. Germanium levels in me teorites range from a few rg/g to >400 rg/g and this would, therefore, be an ideal range of Ge concentrations for the experimental alloys. However, reliable quantitative information from the electron microprobe demands Ge levels 2 0.5 wt% (Goldstein and Yakowitz, 1975). Most alloys. therefore, contained between 0.5 and 1.0 wt% Ge. The bulk P content of the alloy is not critical as long as the alloy remains in they + liquid field at the temperature of interest. For reliable chemical data, a liquid volume fraction greater than -0.2 was desirable. To maintain at least 20% liquid at the equilibration temperature. P levels between 2 and 6 wt% were chosen. (b) The equilibrium experiment: The bulk alloy of a chosen composition was placed in an alumina crucible 2.5 cm long and 1.0 cm in diameter (Coors Porcelain, Colorado). The crucible was then lowered into a vertical tube furnace (Lemont Scientific) in a platinum basket. A schematic drawing of the set-up is shown in Fig. 2. A steady Row of Ar was maintained through the furnace during the experiment to prevent oxidation of the alloy. A Pt-Pt-13% Rh thermocouple was used to monitor the temperature inside the furnace adjacent to the suspended crucible. The temperature was raised to 145O’C for 5 minutes to melt the alloy and then lowered to the equilibration temperature The equilibration temperatures ranged from 1099“C to
SOLIDIFICATION
OF IRON
261
METEORITES
THERMOCOUPLE PLATINUM SUSPENSION WIRE -
i )_
ARGON OUT
otHEATING
ELEMENT
FURNACE TUBE c_
ARGON IN
(-<; f-1: (-QUENCH
VERTICAL
TUBE
TANK
FURNACE
FIG. 2. A schematic drawing of the vertical used for the equilibrium experiments.
tube furnace
137O’C. The alloy was held at the equilibrium temperature for 2 to 4 hours so that the coexisting y and liquid phases would reach equilibrium and was then quenched in water. The quenched sample was sectioned normal to its circular cross-section, mounted in lucite and polished. The surface was etched with 2% nital to reveal the microstructure. Fig. 3 shows a typical microstructure where the large grains are y at the equilibration temperature. The regions of dendritic structure between the y grains were the regions of liquid at the equilibration temperature. The liquid phase solidified
FIG. 4. Position of a typical probe trace across the y phase at the equilibration temperature. S: solid, L: modified liquid, Arrow: indicates the microprobe trace. The alloy had a nominal composition of Fe-14% Ni-2% P-l% Ge and was equilibrated at 1370°C. Bar = 100 em.
as fine dendrites during the quench. Samples that had more than 0.2 volume fraction liquid were used for chemical analyses. (c) Microanalysis of the equilibrated samples: The samples were repolished with 6 zrn and 1 pm diamond paste and etched lightly to help locate areas of interest for microprobe analysis. Quantitative analysis of the solid phase involved several random point analyses on different grains. Homogeneity of the grains was checked by taking a composition trace across a grain. Fig. 4 shows a typical grain that was checked for homogeneity and Fig. 5 shows the com~sitional homogeneity of that grain. A small increase in the P concentration near the edge of the grain is caused by diffusion from the P rich region during the quench. Homogeneity of the grains and the uniform composition of the different grains confirmed equilibrium between the
1 t
04
-
t GRAIN EDGE +
0 FIG. 3. A modified solid (S) + liquid (L) structure obtained on quenching an equilibrated alloy. The alloy had a nominal composition of Fe-lo% Ni-2% P-l% Ge and was equilibrated at 142O’C. Bar = 100 sm.
I
1
20
40
I 60
, 60
I
I 100
I20
140
pm FIG. 5. Com~sitional homogeneity in the solid phase as shown by the electron microprobe trace across a prior y grain shown in Fig. 4.
262
AND J. I. GOLDSTEIN
c‘. NARAYAN
TABU i Typical
data
obtained
from an equilibrium
Fe-9% Ni-2%
P-11.4% Ct: and was equili.brared
-B of analysis
%Ni (wt) In solid
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
8.37 8.25 8.21 8.61 8.46 8.34 a.47 8.26 8.09 8.16 8.08 8.38 8.20 7.90 7.80
Average
t
8.24
in
(wt)
%P
liquid
%P (wt) in liquid
1.015
8.89
+0.004
kO.41
+ 0.03
1099’)C.
P
-
8.04 8.28 9.42 8.82 8.79 9.05 9.16 8.81 8.54 9.10 10.39 8.72 8.27 8.89 9.11
1 .Ol 1.02 1.01 i.01 2.02 I.02 1.02 1.00 1.02 1.02 1.01 1.02 1.02 1.02 0.99
9.86
= 0.84
-_I
_--.5.85 10.01 9.85 10.33 10.18 9.59 9.97 9.56 10.02 9.76 9.82 9.50 9.94 9.35 10.14
%Ge (wt) in solid _... ._._._-_ l.Oi I. 03
I.09 I *i:?l I. 05 i.09 1. 09
I .:I? ! *iI4 i.08 1.08 1.11 1 .il 1 .li, 1 Y04 1.08
-
L
_I.-
K, = 0.114
of
--...-__--
(wt)
in solid
-+0.19
at
-
~I___
%Ni
---
The a1 lay had a !::)mina i :ompo,. i tion
experiment.
-+ 0.005
i .
phases. Composition of the dendritically sohdlhed hquid phase was evaluated through several area scans (40 pm x 50 wrn) and defocused beam analyses (50 pm diameter beam). Small pools of liquid were avoided because their composition could be altered during the quench by the rejection of P by the surrounding grains. The compositions of the solid and the liquid were used to calculate F$. KE and Kt’. RESULTS
The equilibrium experiments were conducted at 1099”C, 1192”C, 1265”C, I3 18°C and i37O”C. Table 1 shows the data obtained from a t-e-Ni-Cie-P sample held at 1099°C for 3 hours. Analyses from 15 regions of former y and liquid phases are given.
The small spread in the compositlon of the soi~ti indicates equilibration at the heat treatment temper, ature. The greater spread in the composition ~11‘the liquid is partially due to the selection of liquid poolh of different sizes. Even within a large pool trf liquid 3 small range of compositions can he t’xpcclt’d tfu~, to sampling differences during area scans ;i~rtl dcfocused beam analyses. The k$’ values cai~latcd from the equilibrium experiments are given ii! ‘I’ahle 2. The functional dependence of @ on the uquillhration temperature is shown in Fig. O. \ leasr squares line drawn through the data points >i&is the following relationship A<;’ ~ ~-3.25 X 10 ’ I : 5.,34 0 ~-
: :>
where T is the temperature in “C. Table I 4s~) i151t the solubility limit of P in the solid at the Itvc cquilibration temperatures.
-1
DISCUSSION (a) Quality oj‘experimentul data. The error in I!ic measured equilibrium partition coefficient Glrise~ from the errors in the measurements of the cumpositions of the solid and the dendriticaily solidified liquid phases. At least 15 random measurements were made on each phase to calculate the range of homogeneity for Ni. P and Ge. The level of homogeneity for a given (1 - a) confidence level ir given hy (Goldstein and Yakowitr, 1975)
FIG. 6. Measured bration temperature.
values
of ti;C a!, a function
of equih-
SOLIDIFICATION
263
OF IRON METEORITES TABLE 2
Dependence
of
Ge KO on the
phosphorus
in 1.02 0.79 0.62 0.43 0.20
1099Oc 1192w 1265 ‘C
i3ia”c 137oOc 15ooOc
and
Ge (wt%) in solid
P (wt%)
T(‘C)
content
solid _+ 0.004 2 0.02 _+ 0.01 _+ 0.02 _+ 0.006 0.00
the
temperature.
in
(wt%) liquid _+ 0.05 _+ 0.04 _+ 0.04 _+ 0.04 _+ 0.03
Ge
1.08
_+ 0.04
1.14 1.10
2 0.02 _+ 0.04
0.78 0.82
_+ 0.03 _+ 0.01
0.67 0.82 0.89 0.81 1.15
solidified
ternary
KGe
0
1.61 _+ 0.14 1.39 _+ 0.07 1.24 _+ 0.07 0.96 _+ 0.06 0.71 _+ 0.02 0.58(*)
I This
data
point
is
taken
from
a dendritically
where WI_, is the range of homogeneity, C is the true concentration of the element in weight fraction, n is the number of measurements, N is the average number of x-ray counts accumulated during each analysis, S, is the standard deviation associated with the total counts, tA-7 is the student t value for (n - 1) degrees of freedom. The term kW,_,/C represents the composition spread around C in relative percent. Table 3 shows the homogeneity data for an alloy equilibrated at 1099°C for 3 hours. The equilibrium partition coefficient Kf is the ratio of the concentration of X in the solid to that in the liquid. If +Rs is the composition spread in the solid phase and fRL that in the liquid phase, both in relative percent, then the range of Kt values is + (Ri + Ri)“’ in relative percent. Table 4 lists KFi, G and @ values for the different temperatures. All error calculations have been made at a 99% confidence level. (b) Effect of Ge content on @. Germanium contents in meteorites range from a few pg/g to >400 pg/g. Reliable quantitative x-ray data from the equilibrium experiments required Ge levels up to 1 wt%. However, Ge concentrations up to 1 wt% do not have any measurable effect on the liquidus and solidus lines of Fe-Ni. Since P influences the solidus and
alloy
Fe-Ni-Ge.
liquidus compositions drastically, its effect on @ can be assumed independent of the bulk Ge content provided that the Ge level is
time
(6)
TABLE 3 Level
of
homogeneity
for
an
Confidence
Element Nickel in Nickel in Phosphorus Phosphorus Germanium Germanium
Solid Liquid in Solid in Liquid in Solid in Liquid
n
+ n-l
15 15 15 15 15 15
2.977 2.977 2.977 2.977 2.977 2.977
alloy
held
Leve 1:
at
1099’C
for
99%.
C&W 0.03 0.03 0.005 0.06 0.05 0.09
3 hours.
a.24 9.86 1.02 8.89 1.08 0.67
X KO
1-U
_+ 0.19 _+ 0.23 2 0.004 + 0.41 _+ 0.04 + 0.05
0.84 0.115 1.61
2 0.03 _+ 0.005 + 0.13
264
C. NARAYAN
AND J. 1. GOLDSTEIN
Table 5 lists the primary dendrite arm spacing (d) and the corresponding solidification time ($) for an Fe-lo% Ni alloy for cooling rates ranging from O.O2”C/sec to l”C/sec. The data have been ab,stracted from Figure 4-3 and Appendix B of Barone rt al., (1964). The ratio of d to the square root of 8, is constant to within 10% with an average value of 26 pm/G. This value together with an estimate for cooling rate in meteoritic parent body cores can be used to estimate primary dendrite arm spacing in parent body cores. If a cooling rate of 1“C per million years (Goldstein and Short, 1967) is assumed for the parent body cores the solidification time is 5 million years and the primary dendrite width would be 325 meters. To get another independent estimate 01‘ the dendrite size in parent bodies Fe-lo% Ni alloys were directionally solidified in the laboratory to yield dendrites aligned with the growth direction. The experiment was carried out for three different solidification times and the results are shown in Table 6. The ratio d/fifis again constant to within 10% with an average value of 59 @m/e. Extrapolation of this data to meteoritic solidification times of 5 million years yields a primary dendrite about 750 meters wide. This estimate is about twice the previous estimate. The difference may be due to the different experimental technique employed in that the dendrite spacing is very sensitive to several experimental parameters (Barone ef al. 1964). Both sets of data. however, indicate that primary dendrites in parent bodies could be typically between 100 and 1000 meters wide. (d) Solid state diffusion in dendrites Dendritic solidification of an alloy leads to the segregation of
the solute element between the dendrite core alrd the dendrite edge. Chemical fractionation of the solute sets up concentration gradients within the dendrite which results in the diffusion of the solute down the concentration gradient. The extent to which solid state diffusion can reduce compositional inhomo geneities depends on the diffusivity (D) of the elcment, the distance over which the solute atom has to diffuse (x) and the time available for diffusion (I). If the diffusivity of the solute elemem is indcpendent of composition or varies only sligbtlq in the composition range being considered, then I he con. centration change due to diffusion is a single valued function of the variable x/21/‘D7 (Reed-Hill, lY7.3). As an example, if two similar alloys are cooled a! two different rates to produce dendrites of sizes 1, and x2 and if t, and t2 are the corresponding timeh available for diffusion in these dendrites, then the changes in the core compositions of these dcndrlteh due to diffusion will be the same if
Work on measurement of partition coefficients from dendritically solidified alloys (Narayan and Goldstein, 1981) indicates that diffusion effects are considerable in 100 pm dendrites in the 500 seconds required for the alloy to cool from if;OO”C tc~ 1000°C. If a cooling rate of I “C per million years (Goldstein and Short, 1967) is assumed for parent body cores then the time for cooling from 1500°C MI 1000°C is 500 million years and equation (8 j prcdiets that diffusion will be considerable in a dendrite that measures 560 meters across. Diffusion corrections are important for elements like Ge and P whose diffusivities in Fe-Ni are higher than 10 ” ~~m’/sec at 1300°C (Narayan and Goldstein, 198 1I. In the previous section primary dendrites in parent body cores were estimated to be typically -500 nteters across. Diffusion corrections are therefore importarlt in modeling segregation of Ge and P in parenr hod&. (e) Simulation of theJractionution o/ m/nor rir.ments in iron meteorite chemical groups. A primal, fractionation model is believed to be responsible for the formation of meteorite parent bodies with I c-Ni cores of uniform compositions corresponding to the average compositions of the chemical groups. When the homogeneous molten Fe-Ni cores solidify tither
SOLIDIFICATION
OF IRON METEORITES
dendritically or with a plane front the attendant segregation together with solid state diffusion effects determine the final trace element concentration distribution within the core. The extent of segregation and diffusion will depend on the freezing mode. During later stages of cooling the segregated asteroids are broken up by collisions. Since, in the event of dendritic solidification, the dendrites could be typically 500 meters across the fragmentation process can result in a number of pieces each several meters across coming from a single dendrite. Fig. 7 is a schematic representation of a possible fragmentation pattern yielding meteorites of a chemical group. Although the figure restricts itself to one primary dendrite, the model can be extended to a parent body where all the primary dendrites upon fragmentation, contribute members of a single chemical group of meteorites. Brody and Flemings (1966) developed a numerical plate mode1 to calculate the segregation profile of a solute element across a dendrite. They characterized the segregation profile with a volume element extending from the dendrite core to the dendrite edge. Fig. 8 is a schematic representation showing the primary dendrites and the volume element chosen for the calculations. The volume element has an infinitesimal thickness parallel to the dendrite growth direction and is divided into a number of layers along the length of the element in the transverse (X) direction. At the start of solidification all the layers are molten (X = 0). With the passage of time the layers solidify successively until all the layers are frozen at the end of solidification (X = L). At any intermediate time, t, each layer solid or liquid is assigned an average composition. The composition of the solid forming at the solid-liquid interface is given
265
b
p$HETEORITES
FROM A
CHEMICAL 0%
IY
f
GROUP
u
i DENDRITE EDGE
DENDRITE CORE
FIG. 7. A schematic drawing showing meteorites from a chemical group can be obtained from different parts of a dendrite.
teorite at a certain distance from the core. The simulated log X vs. log Ni plots can then be compared to the log X vs. log Ni plots developed from observed meteorite compositions. The shape of the simulated
s;a& SOLID 1 LIQUID
I I LIQUID l
-I-,
i
by C; =
K$-Cf
(9)
where Kt is the partition coefficient of element X, Cf is the concentration of the liquid in equilibrium with the solid of concentration C$ forming at the interface. The model assumes complete mixing of the liquid. Therefore throughout the solidification process the composition of all the molten layers is the same. After each stage of solidification the effect of solid state diffusion is calculated in the frozen layers. After complete freezing, diffusion calculations are continued until the temperature reaches 1000°C when the diffusion effects become insignificant. The details of the plate model and the diffusion calculations are discussed by Narayan and Goldstein (1981). For a ternary Fe-Ni-X alloy the solidification and diffusion model cited above will yield the segregation profile of both Ni and the ternary element, X, across the dendrite. The two profiles can be combined on a log X vs. log Ni plot where each point corresponds to a fixed distance from the dendrite core. Each point on this plot can represent the composition of a me-
DISTANCE,
X-
x =0
(DENDRITE
X * Xi
(LIQUID -SOLID
R
CORE)
SOLID
A I
INTERFArE)
+I I LIQUID
L-J
X=L
FIG. 8. The dendrite dendritic
segregation.
(MIDPOINT BETWEEN DENDRITES)
TWO
plate model used to characterize (Brody and Flemings, 1966)
266
C. NARAYAN
plot will depend i)
Equilibrium x,
ii) iii) iv) v)
on the following partition
AND
parameters:
coefficient
of element
K;
Equilibrium partition coefficient of nickel, K:’ Diffusivity of element X in Fe-Ni alloys Diffusivity of nickel in Fe-Ni alloys Starting bulk composition.
Log Ge vs. log Ni plots were developed using the model. The effect of diffusion and the functional dependence of w on the temperature, see equation (3), were both incorporated into the model. The bulk P content and solid state diffusion effects were both important in determining the tinal shape of the simulated plot. Fig. 9 shows curves for two different P levels. The curve marked low P is for an alloy with only -0.05 wt% P and @ is not noticeably changed due to P. This is evident from the straight line generated by the model without diffusion effects. The diffusion effects, however, alter this linear relationship resulting in a line with a decreasing positive slope much like the trend seen in group IVA meteorites. The second curve marked high P has 0.5 wt% P and the effect of P on ?$ is evident by the line changing its slope even before diffusion is considered. Solid state diffusion further modifies this curve to resemble the trend in group IIIAB meteorites. The
A: AFTER
DIFFUSION
B: BEFtRE
DlFFUSlON
HIGH
1 7
B 1 8
P
I
1
I
9
IO
II
NICKEL (wt.%) FIG. 9. Simulation of the general shape of Group IVA with a low P alloy and of Group lIIAB with a high P alloy.
J. 1. GOLDSTEIN
(+) signs indicate the bulk Ge and Ni concentratmns of the two alloys. Having simulated the general trends ill groups IIIAB and IVA an attempt was made to match calculated and measured Ge-Ni variations. The Cie-Nl plot was calculated using the following t’~i1uc:,.
i)
ii)
iii) iv)
Diffusivity
of Ni -= exp[ I. 15 i 0.~:. I k+i ‘%,j
et al., 1965) where C,, is the Ni COIK~~~IT~~~K~I~ Diffusivity of Ge in Fe-Ni -0.492 exp(-61,86O/RT) (Nara>.u-1 :rnd Goldstein, 198 1) Kt’ = 0.87 (Narayan and Goldstein. IO8 i : @ = A function of temperature. rqu;~riun (3).
The bulk compositions were chosen so that the calculated shapes matched the measured Gc-Ni trends. A bulk composition of 8.25% Ni. 0.?5? f” and 38 ppm Ge yielded a reasonable match f;,t group IIIAB while a composition of 8.4% Ni, O.Oj’z,. P and 0. I2 ppm Ge was suited for group IVA. Fig. i 0 shows the calculated and observed trends for the diffusivities, k. values and assumed bulk cornpositrons. The slope reversal that is predicted by the model for group IIIAB meteorites is due to the changing @. As Kri is relatively insensitive to P content (me ‘Table 4) and is always 1. A high P concentration in the bulk alloy causes @ to exceed 1.O very cariy m the freezing process. @ value!, greater than 1.O will result in a negative slope for the simulated Ge-Ni trends. Groups IAB, IIAB and IIICD exhibit such negative slopes as seen in Fig. I, In additior!, i :~uI c‘ should have an effect similar to Y on ?hl; partitioning behavior of Ge since small amounts of these elements also decrease the melting point of t-e-hi alloys. (f) Applicability of the dam to planur ,qrr.m’tA model. The log Ge vs. log Ni plots generated hq :i plane front model and a dendrite model are similar. if diffusion effects are ignored, because the segrc, gation of trace elements during plane front growth and during dendritic growth is characterized by the Scheil equation (equation 2). However, during dendritic growth, chemical inhomogeneities develop over relatively small distances making solid state diffusion considerations important (Narayan and Goldstein. 198 1). Fig. 9 shows the log Ge c’J’.log Ni plot simulated by the dendrite model for a low P Fr-Ni-PGe alloy containing 0.05 wt% P. ‘The low P levei does not influence the @ and the log Ge vs. log Ni trend, before diffusion, is linear and is the same as the trend predicted by the plane front model. However; when diffusion effects are considered the trend hccomcs non-linear and yields a changing positive slope that resembles the observed log Ge KS. log Ni xtriation
SOLIDIFICATION
-
100
SIMULATED OBSERVED
GROUP GROUP
IO f
!k 3
3 8
cooling to 1000°C can experience a fragmentation process. It is possible that the different fragments get trapped in a larger parent body at different depths from the surface. Such an incorporation of smaller bodies in a bigger body has been discussed (Scott, 1979). The exact break up and incorporation sequence is, however, unclear. The fragments buried at different depths will experience different cooling rates when the temperature drops to the Widmanstgtten precipitation range. Such a solidi~cation, fragmentation, incorporation and cooling sequence is consistent with the core model and also allows for meteorites of a given chemical group to have different cooling rates. CONCLUSIONS
I.0
Y
0.i
7
8
9
IO
II
WT. % NICKEL FIG. 10. Matching observed
267
OF IRON METEORITES
data
the calculated Ge-Ni trends with the for meteorites of Groups IIIAB and IVA.
in group IVA (Fig. 1). Fig. 9 also shows a log Ge vs. log Ni plot for a high P (0.5 wt%) Fe-Ni-Ge-P alloy. The curve before diffusion shows a slope reversal and would be similar to the trend predicted by a plane front growth model. Diffusion effects in the dendritic model only modify the shape. For an element like Ir whose diffusivity in Fe-Ni is very low at the solidification temperatures, the diffusion effects are very small (Narayan, 1980). The plane front model and the dendritic model would yield the same range of Ir concentration. For a fast diffusing species like P the dendritic model predicts excessive diffusion effects. The P concentration within a dendrite varies by only a factor 2 which is smaller than the P range seen in group IIIAB. (gf Implications ofthe core model on cooling rate studies. A range of cooling rates observed in a group (Goldstein and Short, 1967; Randich and Goldstein, 1978) appears to contradict the core model for parent bodies. However, all cooling rate investigations are based on the width of the kamacite platelets in the Widmanstatten precipitate. Therefore the cooling rates deduced are valid only in the temperature range 300°C to 700°C where kamacite precipitates in a taenite matrix. The core model on the other hand, refers to the solidification of a molten Fe-Ni core and takes place in the temperature range 1500°C to 1000°C. The parent body after solidification and
(1) Solidification experiments indicate that the effect of P on the partitioning behavior of Ge in FeNi melts is significant in understanding the measured Ge-Ni variations in iron meteorite chemical groups. (2) Computer simulations of the dendritic solidification process indicate that solid state diffusion is a significant factor in the development of chemical fractionation in iron meteorite chemical groups. (3) The Ge-Ni concentration trends predicted by the dendritic solidification process may explain the types of log Ni log Ge curves found for meteorite groups in nature. (4) The dendritic solidification model, including effects of solid state diffusion, should be considered as a viable alternative to the more well known planarfront model for solidification of metallic cores of asteroidal bodies, Acknowle&ments-The authors gratefully acknowledge the financial support provided by NASA through Grant NGR 39-007-043. The authors also wish to thank J. T. Wasson of IJCLA and D. Uhlmann of MIT for their reviews which were very helpful in improving the manuscript,
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C. NARAYAN
AND J. 1. GOLDSTEIN
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Cosmochim.
Acts
37, 1957-
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13(4), 527-546.
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