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Georlnmica et Cosmoeliimiea Acts 1965, Vol. 29, pp. 893 to 920. Pergamon Press Ltd. Printed in Northern Ireland
The growth of the Widmanstatten pattern in metallic meteorites J. I. GOLDSTEIN Smithsonian Astrophysical Observatory, Cambridge, Massachusetts and B. B. OGILVIE Department of Metallurgy, Massachusetts Institute of Technology Cambridge, Massachusetts
(Receiced 30 October 1904) Abstract—The effects of pressure, temperature and time en the formation of the Widsuanstatten pattern found in metallic meteorites have been established. A means of analysis, using the method of finite differences, was developed for the study of the diffusion-controlled growth of the Widmanstatten pattern. The growth analysis accounted for (1) the change of D with Ni concentration; (2) the change of D and the Fe—Ni phase diagram with pressure; (3) the average
meteorite composition; (4) the radius of the parent body and the pressure within it; (5) the degree of undereooling before precipitation took place; and (6) the distance between precipitates. The individual effect of each of these factors was detenuined and displayed in the form of parametric curves. Two cooling models with low internal pressure and two with high internal pressure were examined for the formation of the Widmanstdtten pattern. These models were used to determine the temperature—time relationship in the growth analysis. Excellent agreement between the measured and the calculated taenite composition gradients was found for the low-pressure (< 12 kb) models. The formation of plessite, the development of the two phase structures in ataxites, and the decrease in Ni concentration in the kamaeite near the a/y boundary are all explained in terms of a low-pressure model. INTRODUCTION
METEORITES have since the early 1800’s been actively studied by scientists in such varied fields as chemistry, geology, physics and metallurgy. Metallic meteoritic structures, especially the Widmanstatten pattern, have always fascinated investiga tors who have devoted much effort to learning more about their formation. Metallic meteorites are extremely interesting, since we are dealing with a body that has taken approximately 10 years to cool, has at one time been subjected to pressures great enough to form diamonds, and has certain phase structures that cannot be duplicated in the laboratory. A full explanation of how the meteorite structures formed could contribute to such widely different problems as the origin of cosmic bodies, the process of diamond formation, and the process of nucleation and growth. Temperature, pressure and composition are the important factors determining the meteorite structure. Temperature affects the nucleation of phases and their rate of growth. Since diamonds have been found in a few meteorites, very high pressures must have been present at one period in the development of the meteorite structure. *
Now at Geochemical Laboratory, Goddard Space Flight Center, Oreenbelt, Md. 893
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Among other effects, pressure lowers the diffusion rate at any one temperature and stabilizes the y phase at lower temperatures. Composition is the most important factor in determining phase structures. The nickel content determines the maj or phases present and influences the diffusion and precipitation rates of the major phases. The nature of the Widmanstätten pattern found in metallic meteorites is the key to the size, internal pressure, and thermal history of the parent meteorite body. The main purpose of this study has been to determine under what conditions the Widman stätten pattern formed, by use of an analysis that describes the growth of the pattern as a function of pressure, temperature, and composition. THEORY
Meteorites Theories of the origin of meteorites. Even though meteorites have been studied for many hundreds of years, a generally accepted theory for their origin has not been developed. Any such theory must take into consideration certain established facts about these extraterrestrial bodies (MASON, 1962): (1) The chemical and mineralogical relationships among different classes of meteorites strongly suggest that meteorites were all derived fron; a common parent material. (2) Available data show that meteorite bodies share a common origin with the rest of the solar system. (3) The formation of meteorites can usually be explained by the melting and subsequent differentiation of material of chondritic composition. (4) Iron meteorites have crystallized and cooled very slowly, probably from a large mass of molten Fe—Ni, as is shown by the formation of Widmanstätten patterns in these bodies. (5) Age measurements indicate that the material of the various classes of mete orites crystallized about 45 x 1O years ago. The three chief theories of meteorite origin differ essentially in the postulated diameter of the parent body. The first theory proposes parent bodies that are inter mediate in size between the Moon and the Earth (RINGw00D, 1959; LOVERING, 1957; URLIG, 1954). The second suggests primary bodies the size of the Moon that break up after cooling into secondary bodies of asteroidal size (UREY, 1956; 1958). The third theory postulates parent asteroidal bodies ranging in radius up to 250 km (GOLES and ANDERS, 1961; FISH et at., 1960). RINGWOOD (1961) describes the formation of meteorites thus: A large body, with high internal pressures, was formed and heated by its own radioactivity. It melted partially and differentiated into a metallic core and a chondritic mantle. The body then cooled and a Widmanstätten pattern formed in the Fe—Ni core. After this, the body collided with another body and broke into fragments. This theory would explain the origin of high-pressure cohenite and large-sized diamonds. The necessity for high pressures was also pointed out by UmIG (1954), who postulated that about 105 atmosphere was necessary to prevent the formation of a major Widmanstätten pattern in metallic meteorites having more than 13 wt% Ni. There are a nun;ber of very strong arguments against the high-pressure theory.
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It is difficult to break up a large body without remelting. ALLAN and JACOBS (1956) have also calculated that a body as large as the Moon could not have melted by means of its own radioactivity and still have cooled to a temperature at which the WTidmanstätten pattern could form. Electron-probe microanalysis has shown that Ni. This amount the kamacite phase in octahedrites has about 70 ± 05 of nickel is incompatible with the solubility limits of the kamacite phase at 50,000 atm. Two generations of meteorite bodies have been suggested (PREY, 1959). The original body, according to this theory, was of lunar size or larger and was formed at low temperatures. It then differentiated because of localized heating from various chemical reactions. In the center of the body, under high pressures, diamonds can form. After this process is complete a collision with another body occurs, and several asteroidal-sized bodies are formed. Several objections can be made to this theory: The process requires occurrence of low statistical probability. To break up a body of such a large size without melting is difficult. Also, since most chondrites have a uniform composition, ally theory mvolvmg localized heating aud differeutiation is ruled out. Fisu, Comes and ANBERS (1960) have suggested that asteroidal bodies were formed at low temperatures and were melted by a transient energy source, extinct radioactivity. According to this theory, the differentiation process takes place rapidly, and the Widmanstatten pattern forms as the body cools. The formation of diamonds is explained either by induced shock waves or by a metastable phase resulting from the decomposition of cohenite. Cristobalite, which forms at pressures below 5000 atm, has been found in iron meteorites (MARvIN, 1962), which indicates low pressures. Electron-probe analysis has also shown that the measured a and y interface compositions apparently agree with the solubility limits of the low-pressure diagram at a temperature of 350°C (GOLDSTELN, 1962). The major objections to this theory are that there is no major Widmanstatten pattern in the two-phase ataxites (UHLIG, 1951) and that the high-pressure minerals (diamonds and cohenite) are thermodynamically unstable at low pressures. Classification of metallic meteorites. Metallic meteorites are essentially iron—nickel alloys containing small amounts of cobalt, phosphorus, sulfur, and carbon. The iron— nickel phase diagram (OwEN and Lw, 1949) shown in Fig. 1 can be used in part to explain the general structures that are observed. Meteorites with less than 6 wt % Ni are single-phase kamacite and are called hexahedrites. Meteorites with between 6 and 27 wt% Ni contain two phases, kamacite and taenite; they are divided into two main groups: octahedrites (from 6 to between 11 and 16 wt% Ni) and ataxites Ni). (between 11 and 16 to 27 nucleates ill a Widmanstatten pattern that octahedrites The kamacite phase ill phase in ataxites sometimes nude kamacite The can be seen with the unaided wt%
wt%
eye.
ates ill R Widmansthtten pattern, but generally the precipitation pattern is rather limited in size and can be observed only with a microscope (Fig. 2). Ataxites con taining more than 27 wt% Ni are all taenite.
Formation of the Widmanstatten pattern. The formation of the Widmanstatten pattern in metallic meteorites can he explained qualitatively in terms of the nuclea tion and growth process illustrated in Fig. 3. The parent meteorite body cools very
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slowly. After solidification the metal core consists entirely oftaenite. When a meteorite of 10 wt% Ni forms at low pressures, the kamacite begins to precipitate as the tem perature falls below 700°C. The phase precipitates preferentially along the octa hedral planes of the taenite. As the meteorite continues to cool, both taenite and kamacite must increase in nickel content, but kamacite grows at the expense of taenite hi accordance with the lever rule (650°C). As the temperature decreases still
900-
—
800
—
\
7 TAENITE
w 70O—
—
I—
600—
—
500—
—
a KAMACITE
:::HI.III 0
2
4
6
8
10
I
5
I
I
I
I
20 25 30 WEIGHT PER CENT
35
I
40
I 45
50
NI
Fe—Ni PHASE DIAGRAM
Fig. 1. Iron—nickel phase diagram.
further, the movement of Ni from the /y boundary into the taenite becomes restric ted because of the low diffusion rates. Therefore Ni begins to build up in the taenite phase near the c/y interface (600°C), while the composition at the center of the taenite band remains the same as at higher temperatures (550, 500°C). The final result of this process can be seen in Fig. 4, which shows an electronprobe scan across a typical taenite band. While the meteorites are cooling (550, 500°C), the low Ni areas of the y phase are progressively undercooled below the equilibrium boundary, and precipitation of cc becomes more and more probable. The finely divided + y that forms is called plessite. Figure 5 shows an example of this type of structure. Octahedrites are classified according to the size of their WTidmanstättan patterns (coarse to thie). The width of the cc phase is measured across the phase, perpendicular to the dy interface. Table 1 classifies octahedrites according to size (PERRY, 1944; MASSAISKI, 1962). The two-phase ataxites have a kamacite bandwidth less than that of very fine octahedrites.
0
.
:0
x
o
.
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.4 —
‘2-5
7-4 8-2 9-0 11-65
1-5—2-5 0-5—1-0 0-15—0-4 C w
0 In
D Id,
I0 w
0 1— -J 0 0
0 -J
C)
z
0 F—
.
U
F-
w
z
I-
1•0
o6
0
1500 1000 500 RADIUS OF BODY (km)
0I 2000
Fig. 10. Internal pressures and cooling times for meteoritic bodies.
pressure at the center of the body will also increase. If the density p of the body is uniform, the pressure at the center is given by the equation (BIRcH, 1963):
=
()
0p2r2,
(17)
where 0 is the gravitational constant (6.67 x 10-8 cgs), and r is the radius of the body. We have calculated the internal pressure for a body composed of silicate material and for a body composed of half metal, half silicate material by volume. The values of pressure (atmospheres) versus the radius of the meteoritic body are plotted in Fig. 10. The same graph plots the times necessary for bodies cooling according to Models 1, 2 and 4 to reach 350°C, as a function of the radius of the body.
0
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From this figure we can demonstrate that the maximum internal pressure for a body cooling according to Model 1 is 12,000 atm; according to Model 2, 4,000 atm; and according to Model 4, 45,000 atm. Phase diagram. The compositions of the kamacite (G) and of the interface in the taenite (04”) at a certain temperature are given by the phase diagram. The currently accepted one-atmosphere diagram (OwEN and Lm, 1949) has been modified (GoLD STEIN, 1964). The y/a + y boundary, however, has not been significantly changed; therefore we have used the older diagram. The high-pressure Fe—Ni phase diagram has not yet been measured, but an approximate phase diagram at 50 kb has been calculated (RINuwoon and KAUFMAN, 1962). Using the measured one-atmosphere phase diagram and the calculated 50 kb phase diagram, we can extrapolate the phase diagram at various intermediate pressures. Diffusion coefficients. The rate-controlling factor in the growth of the Widman stätten pattern is the diffusion coefficient in the taenite phase. GOLDSTEIN, HANNE MAN and OGILvIE (1964) have measured these coefficients as a function of composi tion, temperature, and pressure above 80000. The one-atmosphere coefficients can be related as functions of composition (0—50%) and temperature by the equation =
exp (00519C1 ± P15) exp
/76 400 —
11.6G\ PT —
-
(18)
where O is given in atomic ier cent. The effect of pressure (F) on diffusion in the y phase is given by the expression (LAZARUS and NACHTREIB, 1963): =
exp (—PAy/PT),
(19)
where Ar is the activation volume for diffusion. GOLDSTEIN, HANNEMAN and OGILvIE (1964) have also measured the activation volume at 40 kb pressure as a function of composition. By using equations (18) and (19) and the measured values of Ar, we can extrapolate the values of D to the temperature range at which the Widmanstatten pattern forms with an accuracy of * 50 per cent or better. Nucleation temperature and impingement. The temperature at which nucleation of the kamacite phase can take place for a meteorite of a given composition is deter mined by the equilibrium phase diagram. The a phase, however, may not precipitate immediately on entering the two-phase region; in fact, a large amount of undercooling may take place before precipitation begins. In most systems precipitation occurs heterogeneously, first at grain boundaries, then at inclusions. Experiments on polycrystalline Fe—Ni alloys have shown that the precipitation of a, with a corresponding change in composition, does not occur even if the alloys are very slowly cooled. Since meteorites are single-crystal taenite before precipitation of kamacite, the phase was probably formed by a homogeneous nucleation process. It is not unreasonable therefore to assume that some undercooling occurred before precipitation. Since the Widmanstatten pattern nucleates coherently, the negative volume freeenergy term AFV and the positive surface-energy term Aa determine at what
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the precipitate can form. As the temperature decreases, AF becomes negative. Since, however, the lattice parameters of a and y phases change with decreasing temperature and changing interface composition, they will tend to increase the interface coherency strains and thus to increase a (CAHN, 1961). From these considerations, undercooling of 100°C for the precipitation of kamacite in meteorites would not seem mueasonable. The half-width between kamacite platelets (X0) is an impingement index. If two precipitates nucleate close together, the distribution of Ni ill the taenite between two kamacite platelets will be influenced by the growth of both precipitates. By setting 0, we can calculate the build-up of Ni the boundary condition at X = X0, do/dx in the taenite phase from the two competing precipitates. If X0 is large, then little build-up in the taenite will occur, and °Ni at X = X0 is that of the average meteorite composition.
temperature more
EXPERIMENTAL METHODS AND PROCEDURE
Meteorite and preparation for analysis Several studies have been published on the variations in composition of metallic meteorites (M4nINGER and MANNING. 1959; GOLDSTEIN, 1962; YAvNEL et al., 1958). Unfortunately, little use has been made of these data to explain how these structures formed. Since few data are available for meteorites with high Ni contents, we subjected two samples to electron-probe microanalysis. These are: (1) Carlton, a fine octahedrite, 1277 wt% Ni (HENDERSON, 1963), and (2) Dayton, an ataxite, 18.10 wt% Ni (MASON, 1962). Because the growth analysis is based on a plane-front growth, the electron-probe data must be obtained perpendicular to the a/y interface if any correlation is to be made. In this study several a/y interfaces in the Carlton meteorite were oriented perpendicular to the plane of polish before probe analysis. In the Dayton ataxite, the two kamacite areas analyzed were part of the platelets in a Widmanstatten pattern, which indicates that the plane of polish was parallel to an octahedral plane. The correction in the distance scale of the probe scan required to bring the a/y inter face perpendicular to the plane of polish was only S per cent. Before electron-probe microanalysis, we polished these specimens through diamond paste, taking special care to be sure that there were no apparent height differences between the a and ‘ phases. We identified areas of interest with microhardness marks. We used an Applied Research Laboratories electron microanalyzer to measure the Fe and Ni concentrations across the kamacite and taenite phases of the two meteorites. The experimental procedure for obtaining the Fe and Ni X-ray intensi ties and for converting the intensities to composition have already been described (GOLDSTEIN, HANNEMAN and OGILvIE, 1964).
Programming of growth analysis The kamacite growth model was progralnmed in FORTRAN (GOLDSTEIN, 1964) and run on the IBM-7094 computer at MIT. In the analysis we had to assume that in each increment of time t the growth occurred isothermally. In other words, the
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total growth is assumed to be the sum of n isothermal steps. This assumption is valid if the boundary conditions change only slightly in each time increment. The change in the value of C4 was less than 0015 wt% Ni per time increment. If the condition zx2
(0
Dt
is not fulfilled, the finite difference approximation gives undamped oscillations about the solution. In the actual computations the program was designed to test for the condition x2
> 25
(21)
at each iteration. If this condition was not met, the program automatically adjusted the space and time differences to meet the stability requirement. It takes M values of m for the last point in the grid to see the effect of changing the boimdary conditions in the first (m = 1) grid point. Therefore the number of iterations (values of n) near the initial nucleation temperature must be kept large as cooling progresses. In order to accomplish this, we placed a limit on the maximum value of tt so that cooling proceeded no faster than 0O5° per iteration near the nucleation temperature and no faster than O•5° per iteration at lower temperatures. This criterion demands a change in the grid size during the calculations according to equation (21). A change occurs on the average about $ times in the course of the program. Smaller values of the limit (max °C/iteration) used to test the analysis did not increase the accuracy of the program enough to warrant their continued use. Depending on the Ni content of the meteorite, the assumption of infinite diffusion in the phase breaks down below the temperature range where the major growth occurs. Equation (21) gives the criterion for determining when infinite diffusion in the cc phase breaks down. Using values of Dx1* in cc Fe (Bonn and LAI, 1963) for 025 x 106 years/iteration, and zx D, t measured width of the kamacite phase for a given meteorite, noninfinite diffusion sets in about 600°C in a 7% mete orite, 500°C in a 12% meteorite, and 400°C in an 18% meteorite. Even though non-infinite diffusion occurs, the Ni contents in karnacite will still be approximately uniform, since D is still large. Therefore we decided to “cut off” the contribution of CAMA to the mass balance (see equation (10)) at 500°C for the 7% meteorite, at 400°C for the 12% meteorite, and at 350°C for the 18% meteorite. The values of G’ and DIFFA were, however, calculated to a temperature of about 350°C. The basic growth program was easily modified to include (1) the effect of pressure on the one-atmosphere phase diagram; (2) the effect of pressure on the one-atmos phere diffusion coefficients; and (3) the effect of a change in the cooling model. The time of nucleation, average meteorite composition, radius of parent body, and half width between precipitates are all variable. These inputs to the program can be changed at will without changing the basic growth program. EXPERIMENTAL RESULTS
Meteorites Figure 11 shows the results of electron-probe scans made across three selected
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areas in the Canton meteorite. Unlike the other two areas, area 1 showed no build-up of Ni in the middle of the taenite. Since each of the three areas has a different karnacite bandwidth, each one of the kamacite platelets precipitated at different times as the meteorite cooled. Two areas in the Dayton ataxite were analyzed with the probe. Here also, there 50
45
40 H
z 35 0 H
H
z 30 w C)
z
0 C) -J
uJ 25
.
C)
z 20
15
DISTANCE IN MICRONS (I04cm)
fig. 11. Ni distribution in the taenite phase of the Canton meteorite.
was no build-up of Ni in the middle of the taenite phase. The composition of the taenite away from the ci/y interface is equal to the average composition of the meteorite, 17•35 At% Ni. The measured taenite composition at the /y interface in both meteorites was over 35% Ni. Any reasonable extrapolation of the data to the interface would yield values of more than 45% Ni. Growth analysis The reason for developing the growth analysis was to determine under what con ditions the Widn;anstdtten pattern formed in metallic meteorites. A typical Ni concentration distribution curve for the taenite phase, which was calculated from the growth model, is presented in Fig. 12. The build-up of Ni near the /y interface
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820x107 yr COOLING MODEL #2 W00- 76i
w 40 H
120°C
524 xIOTyr R
-
z w z z
200 km
X0
00
NUCLEATION TEMPERATURE=54O°C GROWTH TIME AFTER NUCLEATION tyr)
30
350°C
-
I 5 xl
0
400°C
Q•053 x iO yr
H
z w 0 z
=
20
50°C -
0
0
Composition
z
-i
w
0
xo H—25L.c—-—)
DISTANCE IN MICRONS
Fig. 12. Calculated Ni concentration distribution curve in the taenite phase of the Car-it on meteorite.
in the taenite becomes significant only at temperatures below 450°C. Below this temperature the diffusion rates are very low. In fact, between the c/y interface and one micron away in the taenite,the Ni concentration changes from 48 At% to 35 At %. We should note that the major growth occurs in the first 50—100°C of cooling after precipitation occurs. An analysis of the relative effects of all the variables that influence the growth process will now be presented. For each of the three cooling models investigated, the major variables are (1) the average meteorite composition G; (2) the radius B of the parent body and the pressure F within it; (3) the amount of undercooling T before precipitation; and (4) the distance X0 between precipitates. These variables fall in a hierarchy of importance from 1 to 4. Table 3 gives the effect of meteorite composition on the kamacite width calculated Table 3. Calculated widths of the kamacite hands as a function of meteorite composition Meteorite Canyon Diablo (coarse octahedrite) Canton (finest octahedrite) Dayton (ataxite)
Average meteorite Calculated kamacite composition (C0)(wt% Ni) widths (W) (miii) 725
> 25
12-77
010
1810
0012
Variables held constant Cooling model #1 1? = 250 km T = 1000 V
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OGILVIE
from the growth analysis. The relation of TV to G shown in the table clearly demon strates that the kamacite width decreases as the Ni concentration in the meteorite increases. The effects of the radius of the parent body and the amount of undercooling on the calculated width of the kamacite bands are shown in Fig. 13. This figure demon strates, by the use of parametric curves, the relation between T’V, B and AT for Model 1 and the Carlton meteorite. For bodies with radii of 500 1cm, the maximum internal pressures are 4 kb; for those with 800 km radii, 10 kb. This figure clearly U) C
0
ci
S .2..
500
fi 400
-o
300 C
200 0 C
S
C
00
0
100
200
300 400 500 600 700 Radius of Potent Body (km)
800
Fig. 13. Kamacite bandwidth versus radius of parent body, Modo 1.
.
demonstrates the effect of 10 kb pressure on the width of the kamacite phase, a lowering of both the equilibrium precipitation temperature and the interdiffusion coefficients. The distance between kamacite platelets (X0) becomes very important when X0 is less than twice the width of the kamacite band. The effect of X0 on the calculated kamacite width is shown in Fig. 14, where the ratio of the kamacite width calculated (TV9/W) is plotted for a given X0 to the kamacite width calculated for X0 X0( TV0/X0). If W,0/X0 is against the ratio of the calculated kamacitc width to greater than about 0-3, the effect of X0 on TV0 must be considered. area in one meteorite, the amount of undercooling necessary at a For one given B can be determined by using parametric curves similar to those in Figs. 13 and 14. The growth analysis can then be used to calculate the curves of composition rersus distance in the taenitc. A comparison of electron-probe data and the calculated Ni distribution curve can then be made and the comparison used to determine whether one unique set of conditions exists for the growth of the kamacite plate. The parametric method of analysis can be extended for usc in other —y areas in the same meteorite and for use in areas in more than one meteorite. It can also be used to determine the validity of the different cooling models proposed. Four values of B and AT, which give a calculated kamacite bandwidth the same size as that for Area 1 in the Carlton meteorite (Fig. 11), were determined (Model 1).
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The concentration gradients cal The kamacite band is 75 wide, and X0 culated for the four different-sized bodies by means of the growth analysis are shown in Fig. 15. It is apparent that the 100 km body does not give the correct concentra tion gradient in taenite. A good fit is, however, obtained for B = 250, 500, and $00 km. It appears that for cooling Model 1 no unique radius for the parent mete orite body exists. We confirmed this conclusion by a similar analysis for the —y areas in the Dayton meteorite. We should note, however, that according to this model, the maximum allowable pressure was 12 kb. .
I•0
08
O6
8 :04
O2
0 0
O2
04
06
08
1•0
wxo/ xo Fig. 14. Effect of X0 on the width of the kamacite band.
The parametric technique was also used to determine the combinations of B and 1T for this same area in the Canton meteorite for Model 2. The calculated con centration gradients for B = 100, 200 and 500 km are plotted in Fig. 16. For this cooling model a unique fit of concentration versus distance is obtained at B = 200 km. To test this solution (B = 200 krn), we calculated G vs. X in the taenite phase for Areas 1, 2 and 3 in the Carlton meteorite. The calculated curves are shown in Fig. 17. The agreement is very close. Note that as the amount of undercooling decreases, the value of 1V increases. Also, the calculated concentration distribution curves above 30% Ni are unaffected by the amount of undercooling. If a unique radius of 200 kin exists for the parent meteorite body, then the con centration distribution curves calculated by this model for meteorites other than the Carlton should agree with measured probe data from those meteorites. The growth analysis was applied to three different meteorites, Canyon Diablo, Carlton and Dayton. The Canyon Diablo scan had already been measured (GoLDsTEIN, 1962), and the distance scale was adjusted so that the scan was taken perpendicular to the /y interface. The results of the calculations are shown in Fig. 1$. The measured and calculated distribution curves fit very closely. The analysis shows that the Widman stätten pattern in meteorites, from the coarsest octahednites to the finest ataxites, could have been formed from one or several parent bodies at low pressures. We have also investigated cooling Model 4. Of particular interest here are bodies whose internal pressures are high, 25 and 40 kb. Even if no undercooling occurs
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before precipitation, the maximum bandwidth is calculated to be 3 jc at 40 kb, and 32 at 25 kb for the Carlton meteorite. Most of the measured values of JV in the Canton are over 100 t. Internal pressures of this order of magnitude are therefore not reasonable under any conditions. The two measured inputs for the growth analysis were the Fe—Ni phase diagram 50
45 MODEL#I CARLTON METEORITE W— 75±
40 H ci
z 0
R° a R° V R R=
35
100 km, AT 55°C 250 km, AT = 115°C 500 km, AT ° 25°C, P=4kb 800 ka, AT = 90°C, P ° 10kb
H
z LU
C
z
0
C -J LU C
25
z
.
20 sured Curve
I5
DISTANCE IN MICRONS
Fig. 15. Calculated and measured composition distribution curves in taenite, Model 1.
and the Fe—Ni interdiffusion coefficients. The growth analysis was tested to see what effect the errors in the determination of C+1 and D had on the calculated values of flT A systematic error in G’ of +05 i\t% or about 5°C in the nucleation tem perature yields an uncertainty in W of only 6 per cent. A systematic error in G+ of + P0 At % or about +10°C in the nucleation temperature yields an uncertainty in TV of only 14 per cent. An uncertainty of +25 per cent in the extrapolated dif fusion coefficients yields an uncertainty of 10 per cent in TTT; of +50 per cent, an uncertainty of 20 per cent in W. These errors are small. They affect the resultant °Ni vs. X The extrapolated 13 values from an early diffusion study of the Fe—Ni system (WELLs and MEJa, 1941) were also used in order to see what effect they had on the calculated values of TV. The Wells and Mehl values of D had the effect of increasing TV by over 300 per cent. curves
to
a
much
smaller
degree
than the
errors
in
I
TV predict.
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DISCUSSION
We have used the growth analysis to determine the Ni distribution in taenite and to determine the kamacite bandwidths in metallic meteorites. The results of the growth analysis were compared with the measured Ni distribution in taenite from electron-probe microanalysis. We have also determined the effect of the variables that influence the growth process. The errors in the mcasurement of the interdiffusion 50
45
40 H 2 0
35
or H 2
w
U 2 0 U -J U
30
sr 25
U 2
20
IS
DISTANCE IN MICRONS
Fig. 16. Calculated
and measured composition distribution curves in taenite, Model 2.
coefficient, the Fe—Ni phase diagram, and the error resulting from variation of ther mal diffnsivity a with temperature cause only a small error in the growth analysis. Several conclusions can be drawn from the results of this work about the forma tion of the Widmanstatten pattern in metallic meteorites. The value of the Ni con centration in taenite at the a/p boundary has not been measured very accurately with the electron probe. The values reported to date lie between 35 and 45% Ni, depending on the investigator and the electron-probe used. The growth analysis shows that a steep Ni gradient exists in the taenite near the a/p boundary. In fact, the calculated Ni concentration varies from 35 to 50 per cent within the first micron of the taenite phase. Since the X-ray resolution of the electron probe is at best one
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micron, only an average value of G should be expected at the /y boundary. There fore the Ni concentration in taenite at the o/y boundary is probably close to 50 per cent. The Ni conceiltration in kamacite is uniform, except near the c/y boundary, where a decrease of up to 1 per cent is observed (AGRELL, LoNG and OGILvIE, 1963). Several 50
45
40
z
MODEL #2 CARLTON METEORITE RADIUS= 200 km
35
• Area I, W 75, AT l20°C,W/X o o Area 2,W 90u, AT Il0°C,W/X0049 Area 3,Wo l25, AT o95°C, W/X,044
0
H
z 30 w U z 0
U
-J
w 25
.
U
z 20 Curves Meteorite
I0 5,tu
DISTANCE IN MICRONS t104cm)
Fig. 17. Calculated and measured composition curves in taenite in 3 areas, Model 2.
theories have been proposed to explain the decrease. The simplest of these involves the bending back of the + y boundary of the one-atmosphere phase diagram at low temperatures. As the meteorite cools below 400°C, the value of the Ni content in the phase at the cd/y boundary will decrease. This causes the taenite to begin to grow with respect to the kamacite. Because nickel is rejected from the phase and D5 is no longer infinite, a gradient of Ni will develop at the border of the /y interface. Unfortunately, the Fe—Ni diagram is not accurately known below 500°C. An analysis of the X-ray data (OWEN and Liu, 1949; OWEN and SULLY, 1939) taken below 500°C indicates, however, that the o’./ + y boundary probably bends back at about 400°C. Therefore the Ni concentration of the and y phases at the interface indicate a final growth temperature of about 350°C at low pressures.
4
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The growth of the WTidmanstdtten pattern in metallic meteorites
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That no Widmanstatten pattern is present in meteorites containing more than 13 wt% Ni has led Firno (1954) to postulate that pressure was the factor that pre vented its formation. Uhlig argues that pressure serves to lower the transformation phase will precipitate at temperatures where temperature, y n + y, so that the the diffusion of Ni in taenite is insufficient to allow the Widmanstatten structure to —÷
form (
Georlnmica et Cosmoeliimiea Acts 1965, Vol. 29, pp. 893 to 920. Pergamon Press Ltd. Printed in Northern Ireland
The growth of the Widmanstatten pattern in metallic meteorites J. I. GOLDSTEIN Smithsonian Astrophysical Observatory, Cambridge, Massachusetts and B. B. OGILVIE Department of Metallurgy, Massachusetts Institute of Technology Cambridge, Massachusetts
(Receiced 30 October 1904) Abstract—The effects of pressure, temperature and time en the formation of the Widsuanstatten pattern found in metallic meteorites have been established. A means of analysis, using the method of finite differences, was developed for the study of the diffusion-controlled growth of the Widmanstatten pattern. The growth analysis accounted for (1) the change of D with Ni concentration; (2) the change of D and the Fe—Ni phase diagram with pressure; (3) the average
meteorite composition; (4) the radius of the parent body and the pressure within it; (5) the degree of undereooling before precipitation took place; and (6) the distance between precipitates. The individual effect of each of these factors was detenuined and displayed in the form of parametric curves. Two cooling models with low internal pressure and two with high internal pressure were examined for the formation of the Widmanstdtten pattern. These models were used to determine the temperature—time relationship in the growth analysis. Excellent agreement between the measured and the calculated taenite composition gradients was found for the low-pressure (< 12 kb) models. The formation of plessite, the development of the two phase structures in ataxites, and the decrease in Ni concentration in the kamaeite near the a/y boundary are all explained in terms of a low-pressure model. INTRODUCTION
METEORITES have since the early 1800’s been actively studied by scientists in such varied fields as chemistry, geology, physics and metallurgy. Metallic meteoritic structures, especially the Widmanstatten pattern, have always fascinated investiga tors who have devoted much effort to learning more about their formation. Metallic meteorites are extremely interesting, since we are dealing with a body that has taken approximately 10 years to cool, has at one time been subjected to pressures great enough to form diamonds, and has certain phase structures that cannot be duplicated in the laboratory. A full explanation of how the meteorite structures formed could contribute to such widely different problems as the origin of cosmic bodies, the process of diamond formation, and the process of nucleation and growth. Temperature, pressure and composition are the important factors determining the meteorite structure. Temperature affects the nucleation of phases and their rate of growth. Since diamonds have been found in a few meteorites, very high pressures must have been present at one period in the development of the meteorite structure. *
Now at Geochemical Laboratory, Goddard Space Flight Center, Oreenbelt, Md. 893
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Among other effects, pressure lowers the diffusion rate at any one temperature and stabilizes the y phase at lower temperatures. Composition is the most important factor in determining phase structures. The nickel content determines the maj or phases present and influences the diffusion and precipitation rates of the major phases. The nature of the Widmanstätten pattern found in metallic meteorites is the key to the size, internal pressure, and thermal history of the parent meteorite body. The main purpose of this study has been to determine under what conditions the Widman stätten pattern formed, by use of an analysis that describes the growth of the pattern as a function of pressure, temperature, and composition. THEORY
Meteorites Theories of the origin of meteorites. Even though meteorites have been studied for many hundreds of years, a generally accepted theory for their origin has not been developed. Any such theory must take into consideration certain established facts about these extraterrestrial bodies (MASON, 1962): (1) The chemical and mineralogical relationships among different classes of meteorites strongly suggest that meteorites were all derived fron; a common parent material. (2) Available data show that meteorite bodies share a common origin with the rest of the solar system. (3) The formation of meteorites can usually be explained by the melting and subsequent differentiation of material of chondritic composition. (4) Iron meteorites have crystallized and cooled very slowly, probably from a large mass of molten Fe—Ni, as is shown by the formation of Widmanstätten patterns in these bodies. (5) Age measurements indicate that the material of the various classes of mete orites crystallized about 45 x 1O years ago. The three chief theories of meteorite origin differ essentially in the postulated diameter of the parent body. The first theory proposes parent bodies that are inter mediate in size between the Moon and the Earth (RINGw00D, 1959; LOVERING, 1957; URLIG, 1954). The second suggests primary bodies the size of the Moon that break up after cooling into secondary bodies of asteroidal size (UREY, 1956; 1958). The third theory postulates parent asteroidal bodies ranging in radius up to 250 km (GOLES and ANDERS, 1961; FISH et at., 1960). RINGWOOD (1961) describes the formation of meteorites thus: A large body, with high internal pressures, was formed and heated by its own radioactivity. It melted partially and differentiated into a metallic core and a chondritic mantle. The body then cooled and a Widmanstätten pattern formed in the Fe—Ni core. After this, the body collided with another body and broke into fragments. This theory would explain the origin of high-pressure cohenite and large-sized diamonds. The necessity for high pressures was also pointed out by UmIG (1954), who postulated that about 105 atmosphere was necessary to prevent the formation of a major Widmanstätten pattern in metallic meteorites having more than 13 wt% Ni. There are a nun;ber of very strong arguments against the high-pressure theory.
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It is difficult to break up a large body without remelting. ALLAN and JACOBS (1956) have also calculated that a body as large as the Moon could not have melted by means of its own radioactivity and still have cooled to a temperature at which the WTidmanstätten pattern could form. Electron-probe microanalysis has shown that Ni. This amount the kamacite phase in octahedrites has about 70 ± 05 of nickel is incompatible with the solubility limits of the kamacite phase at 50,000 atm. Two generations of meteorite bodies have been suggested (PREY, 1959). The original body, according to this theory, was of lunar size or larger and was formed at low temperatures. It then differentiated because of localized heating from various chemical reactions. In the center of the body, under high pressures, diamonds can form. After this process is complete a collision with another body occurs, and several asteroidal-sized bodies are formed. Several objections can be made to this theory: The process requires occurrence of low statistical probability. To break up a body of such a large size without melting is difficult. Also, since most chondrites have a uniform composition, ally theory mvolvmg localized heating aud differeutiation is ruled out. Fisu, Comes and ANBERS (1960) have suggested that asteroidal bodies were formed at low temperatures and were melted by a transient energy source, extinct radioactivity. According to this theory, the differentiation process takes place rapidly, and the Widmanstatten pattern forms as the body cools. The formation of diamonds is explained either by induced shock waves or by a metastable phase resulting from the decomposition of cohenite. Cristobalite, which forms at pressures below 5000 atm, has been found in iron meteorites (MARvIN, 1962), which indicates low pressures. Electron-probe analysis has also shown that the measured a and y interface compositions apparently agree with the solubility limits of the low-pressure diagram at a temperature of 350°C (GOLDSTELN, 1962). The major objections to this theory are that there is no major Widmanstatten pattern in the two-phase ataxites (UHLIG, 1951) and that the high-pressure minerals (diamonds and cohenite) are thermodynamically unstable at low pressures. Classification of metallic meteorites. Metallic meteorites are essentially iron—nickel alloys containing small amounts of cobalt, phosphorus, sulfur, and carbon. The iron— nickel phase diagram (OwEN and Lw, 1949) shown in Fig. 1 can be used in part to explain the general structures that are observed. Meteorites with less than 6 wt % Ni are single-phase kamacite and are called hexahedrites. Meteorites with between 6 and 27 wt% Ni contain two phases, kamacite and taenite; they are divided into two main groups: octahedrites (from 6 to between 11 and 16 wt% Ni) and ataxites Ni). (between 11 and 16 to 27 nucleates ill a Widmanstatten pattern that octahedrites The kamacite phase ill phase in ataxites sometimes nude kamacite The can be seen with the unaided wt%
wt%
eye.
ates ill R Widmansthtten pattern, but generally the precipitation pattern is rather limited in size and can be observed only with a microscope (Fig. 2). Ataxites con taining more than 27 wt% Ni are all taenite.
Formation of the Widmanstatten pattern. The formation of the Widmanstatten pattern in metallic meteorites can he explained qualitatively in terms of the nuclea tion and growth process illustrated in Fig. 3. The parent meteorite body cools very
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slowly. After solidification the metal core consists entirely oftaenite. When a meteorite of 10 wt% Ni forms at low pressures, the kamacite begins to precipitate as the tem perature falls below 700°C. The phase precipitates preferentially along the octa hedral planes of the taenite. As the meteorite continues to cool, both taenite and kamacite must increase in nickel content, but kamacite grows at the expense of taenite hi accordance with the lever rule (650°C). As the temperature decreases still
900-
—
800
—
\
7 TAENITE
w 70O—
—
I—
600—
—
500—
—
a KAMACITE
:::HI.III 0
2
4
6
8
10
I
5
I
I
I
I
20 25 30 WEIGHT PER CENT
35
I
40
I 45
50
NI
Fe—Ni PHASE DIAGRAM
Fig. 1. Iron—nickel phase diagram.
further, the movement of Ni from the /y boundary into the taenite becomes restric ted because of the low diffusion rates. Therefore Ni begins to build up in the taenite phase near the c/y interface (600°C), while the composition at the center of the taenite band remains the same as at higher temperatures (550, 500°C). The final result of this process can be seen in Fig. 4, which shows an electronprobe scan across a typical taenite band. While the meteorites are cooling (550, 500°C), the low Ni areas of the y phase are progressively undercooled below the equilibrium boundary, and precipitation of cc becomes more and more probable. The finely divided + y that forms is called plessite. Figure 5 shows an example of this type of structure. Octahedrites are classified according to the size of their WTidmanstättan patterns (coarse to thie). The width of the cc phase is measured across the phase, perpendicular to the dy interface. Table 1 classifies octahedrites according to size (PERRY, 1944; MASSAISKI, 1962). The two-phase ataxites have a kamacite bandwidth less than that of very fine octahedrites.
0
.
:0
x
o
.
.
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.4 —
‘2-5
7-4 8-2 9-0 11-65
1-5—2-5 0-5—1-0 0-15—0-4 C w
0 In
D Id,
I0 w
0 1— -J 0 0
0 -J
C)
z
0 F—
.
U
F-
w
z
I-
1•0
o6
0
1500 1000 500 RADIUS OF BODY (km)
0I 2000
Fig. 10. Internal pressures and cooling times for meteoritic bodies.
pressure at the center of the body will also increase. If the density p of the body is uniform, the pressure at the center is given by the equation (BIRcH, 1963):
=
()
0p2r2,
(17)
where 0 is the gravitational constant (6.67 x 10-8 cgs), and r is the radius of the body. We have calculated the internal pressure for a body composed of silicate material and for a body composed of half metal, half silicate material by volume. The values of pressure (atmospheres) versus the radius of the meteoritic body are plotted in Fig. 10. The same graph plots the times necessary for bodies cooling according to Models 1, 2 and 4 to reach 350°C, as a function of the radius of the body.
0
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From this figure we can demonstrate that the maximum internal pressure for a body cooling according to Model 1 is 12,000 atm; according to Model 2, 4,000 atm; and according to Model 4, 45,000 atm. Phase diagram. The compositions of the kamacite (G) and of the interface in the taenite (04”) at a certain temperature are given by the phase diagram. The currently accepted one-atmosphere diagram (OwEN and Lm, 1949) has been modified (GoLD STEIN, 1964). The y/a + y boundary, however, has not been significantly changed; therefore we have used the older diagram. The high-pressure Fe—Ni phase diagram has not yet been measured, but an approximate phase diagram at 50 kb has been calculated (RINuwoon and KAUFMAN, 1962). Using the measured one-atmosphere phase diagram and the calculated 50 kb phase diagram, we can extrapolate the phase diagram at various intermediate pressures. Diffusion coefficients. The rate-controlling factor in the growth of the Widman stätten pattern is the diffusion coefficient in the taenite phase. GOLDSTEIN, HANNE MAN and OGILvIE (1964) have measured these coefficients as a function of composi tion, temperature, and pressure above 80000. The one-atmosphere coefficients can be related as functions of composition (0—50%) and temperature by the equation =
exp (00519C1 ± P15) exp
/76 400 —
11.6G\ PT —
-
(18)
where O is given in atomic ier cent. The effect of pressure (F) on diffusion in the y phase is given by the expression (LAZARUS and NACHTREIB, 1963): =
exp (—PAy/PT),
(19)
where Ar is the activation volume for diffusion. GOLDSTEIN, HANNEMAN and OGILvIE (1964) have also measured the activation volume at 40 kb pressure as a function of composition. By using equations (18) and (19) and the measured values of Ar, we can extrapolate the values of D to the temperature range at which the Widmanstatten pattern forms with an accuracy of * 50 per cent or better. Nucleation temperature and impingement. The temperature at which nucleation of the kamacite phase can take place for a meteorite of a given composition is deter mined by the equilibrium phase diagram. The a phase, however, may not precipitate immediately on entering the two-phase region; in fact, a large amount of undercooling may take place before precipitation begins. In most systems precipitation occurs heterogeneously, first at grain boundaries, then at inclusions. Experiments on polycrystalline Fe—Ni alloys have shown that the precipitation of a, with a corresponding change in composition, does not occur even if the alloys are very slowly cooled. Since meteorites are single-crystal taenite before precipitation of kamacite, the phase was probably formed by a homogeneous nucleation process. It is not unreasonable therefore to assume that some undercooling occurred before precipitation. Since the Widmanstatten pattern nucleates coherently, the negative volume freeenergy term AFV and the positive surface-energy term Aa determine at what
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the precipitate can form. As the temperature decreases, AF becomes negative. Since, however, the lattice parameters of a and y phases change with decreasing temperature and changing interface composition, they will tend to increase the interface coherency strains and thus to increase a (CAHN, 1961). From these considerations, undercooling of 100°C for the precipitation of kamacite in meteorites would not seem mueasonable. The half-width between kamacite platelets (X0) is an impingement index. If two precipitates nucleate close together, the distribution of Ni ill the taenite between two kamacite platelets will be influenced by the growth of both precipitates. By setting 0, we can calculate the build-up of Ni the boundary condition at X = X0, do/dx in the taenite phase from the two competing precipitates. If X0 is large, then little build-up in the taenite will occur, and °Ni at X = X0 is that of the average meteorite composition.
temperature more
EXPERIMENTAL METHODS AND PROCEDURE
Meteorite and preparation for analysis Several studies have been published on the variations in composition of metallic meteorites (M4nINGER and MANNING. 1959; GOLDSTEIN, 1962; YAvNEL et al., 1958). Unfortunately, little use has been made of these data to explain how these structures formed. Since few data are available for meteorites with high Ni contents, we subjected two samples to electron-probe microanalysis. These are: (1) Carlton, a fine octahedrite, 1277 wt% Ni (HENDERSON, 1963), and (2) Dayton, an ataxite, 18.10 wt% Ni (MASON, 1962). Because the growth analysis is based on a plane-front growth, the electron-probe data must be obtained perpendicular to the a/y interface if any correlation is to be made. In this study several a/y interfaces in the Carlton meteorite were oriented perpendicular to the plane of polish before probe analysis. In the Dayton ataxite, the two kamacite areas analyzed were part of the platelets in a Widmanstatten pattern, which indicates that the plane of polish was parallel to an octahedral plane. The correction in the distance scale of the probe scan required to bring the a/y inter face perpendicular to the plane of polish was only S per cent. Before electron-probe microanalysis, we polished these specimens through diamond paste, taking special care to be sure that there were no apparent height differences between the a and ‘ phases. We identified areas of interest with microhardness marks. We used an Applied Research Laboratories electron microanalyzer to measure the Fe and Ni concentrations across the kamacite and taenite phases of the two meteorites. The experimental procedure for obtaining the Fe and Ni X-ray intensi ties and for converting the intensities to composition have already been described (GOLDSTEIN, HANNEMAN and OGILvIE, 1964).
Programming of growth analysis The kamacite growth model was progralnmed in FORTRAN (GOLDSTEIN, 1964) and run on the IBM-7094 computer at MIT. In the analysis we had to assume that in each increment of time t the growth occurred isothermally. In other words, the
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total growth is assumed to be the sum of n isothermal steps. This assumption is valid if the boundary conditions change only slightly in each time increment. The change in the value of C4 was less than 0015 wt% Ni per time increment. If the condition zx2
(0
Dt
is not fulfilled, the finite difference approximation gives undamped oscillations about the solution. In the actual computations the program was designed to test for the condition x2
> 25
(21)
at each iteration. If this condition was not met, the program automatically adjusted the space and time differences to meet the stability requirement. It takes M values of m for the last point in the grid to see the effect of changing the boimdary conditions in the first (m = 1) grid point. Therefore the number of iterations (values of n) near the initial nucleation temperature must be kept large as cooling progresses. In order to accomplish this, we placed a limit on the maximum value of tt so that cooling proceeded no faster than 0O5° per iteration near the nucleation temperature and no faster than O•5° per iteration at lower temperatures. This criterion demands a change in the grid size during the calculations according to equation (21). A change occurs on the average about $ times in the course of the program. Smaller values of the limit (max °C/iteration) used to test the analysis did not increase the accuracy of the program enough to warrant their continued use. Depending on the Ni content of the meteorite, the assumption of infinite diffusion in the phase breaks down below the temperature range where the major growth occurs. Equation (21) gives the criterion for determining when infinite diffusion in the cc phase breaks down. Using values of Dx1* in cc Fe (Bonn and LAI, 1963) for 025 x 106 years/iteration, and zx D, t measured width of the kamacite phase for a given meteorite, noninfinite diffusion sets in about 600°C in a 7% mete orite, 500°C in a 12% meteorite, and 400°C in an 18% meteorite. Even though non-infinite diffusion occurs, the Ni contents in karnacite will still be approximately uniform, since D is still large. Therefore we decided to “cut off” the contribution of CAMA to the mass balance (see equation (10)) at 500°C for the 7% meteorite, at 400°C for the 12% meteorite, and at 350°C for the 18% meteorite. The values of G’ and DIFFA were, however, calculated to a temperature of about 350°C. The basic growth program was easily modified to include (1) the effect of pressure on the one-atmosphere phase diagram; (2) the effect of pressure on the one-atmos phere diffusion coefficients; and (3) the effect of a change in the cooling model. The time of nucleation, average meteorite composition, radius of parent body, and half width between precipitates are all variable. These inputs to the program can be changed at will without changing the basic growth program. EXPERIMENTAL RESULTS
Meteorites Figure 11 shows the results of electron-probe scans made across three selected
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areas in the Canton meteorite. Unlike the other two areas, area 1 showed no build-up of Ni in the middle of the taenite. Since each of the three areas has a different karnacite bandwidth, each one of the kamacite platelets precipitated at different times as the meteorite cooled. Two areas in the Dayton ataxite were analyzed with the probe. Here also, there 50
45
40 H
z 35 0 H
H
z 30 w C)
z
0 C) -J
uJ 25
.
C)
z 20
15
DISTANCE IN MICRONS (I04cm)
fig. 11. Ni distribution in the taenite phase of the Canton meteorite.
was no build-up of Ni in the middle of the taenite phase. The composition of the taenite away from the ci/y interface is equal to the average composition of the meteorite, 17•35 At% Ni. The measured taenite composition at the /y interface in both meteorites was over 35% Ni. Any reasonable extrapolation of the data to the interface would yield values of more than 45% Ni. Growth analysis The reason for developing the growth analysis was to determine under what con ditions the Widn;anstdtten pattern formed in metallic meteorites. A typical Ni concentration distribution curve for the taenite phase, which was calculated from the growth model, is presented in Fig. 12. The build-up of Ni near the /y interface
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820x107 yr COOLING MODEL #2 W00- 76i
w 40 H
120°C
524 xIOTyr R
-
z w z z
200 km
X0
00
NUCLEATION TEMPERATURE=54O°C GROWTH TIME AFTER NUCLEATION tyr)
30
350°C
-
I 5 xl
0
400°C
Q•053 x iO yr
H
z w 0 z
=
20
50°C -
0
0
Composition
z
-i
w
0
xo H—25L.c—-—)
DISTANCE IN MICRONS
Fig. 12. Calculated Ni concentration distribution curve in the taenite phase of the Car-it on meteorite.
in the taenite becomes significant only at temperatures below 450°C. Below this temperature the diffusion rates are very low. In fact, between the c/y interface and one micron away in the taenite,the Ni concentration changes from 48 At% to 35 At %. We should note that the major growth occurs in the first 50—100°C of cooling after precipitation occurs. An analysis of the relative effects of all the variables that influence the growth process will now be presented. For each of the three cooling models investigated, the major variables are (1) the average meteorite composition G; (2) the radius B of the parent body and the pressure F within it; (3) the amount of undercooling T before precipitation; and (4) the distance X0 between precipitates. These variables fall in a hierarchy of importance from 1 to 4. Table 3 gives the effect of meteorite composition on the kamacite width calculated Table 3. Calculated widths of the kamacite hands as a function of meteorite composition Meteorite Canyon Diablo (coarse octahedrite) Canton (finest octahedrite) Dayton (ataxite)
Average meteorite Calculated kamacite composition (C0)(wt% Ni) widths (W) (miii) 725
> 25
12-77
010
1810
0012
Variables held constant Cooling model #1 1? = 250 km T = 1000 V
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OGILVIE
from the growth analysis. The relation of TV to G shown in the table clearly demon strates that the kamacite width decreases as the Ni concentration in the meteorite increases. The effects of the radius of the parent body and the amount of undercooling on the calculated width of the kamacite bands are shown in Fig. 13. This figure demon strates, by the use of parametric curves, the relation between T’V, B and AT for Model 1 and the Carlton meteorite. For bodies with radii of 500 1cm, the maximum internal pressures are 4 kb; for those with 800 km radii, 10 kb. This figure clearly U) C
0
ci
S .2..
500
fi 400
-o
300 C
200 0 C
S
C
00
0
100
200
300 400 500 600 700 Radius of Potent Body (km)
800
Fig. 13. Kamacite bandwidth versus radius of parent body, Modo 1.
.
demonstrates the effect of 10 kb pressure on the width of the kamacite phase, a lowering of both the equilibrium precipitation temperature and the interdiffusion coefficients. The distance between kamacite platelets (X0) becomes very important when X0 is less than twice the width of the kamacite band. The effect of X0 on the calculated kamacite width is shown in Fig. 14, where the ratio of the kamacite width calculated (TV9/W) is plotted for a given X0 to the kamacite width calculated for X0 X0( TV0/X0). If W,0/X0 is against the ratio of the calculated kamacitc width to greater than about 0-3, the effect of X0 on TV0 must be considered. area in one meteorite, the amount of undercooling necessary at a For one given B can be determined by using parametric curves similar to those in Figs. 13 and 14. The growth analysis can then be used to calculate the curves of composition rersus distance in the taenitc. A comparison of electron-probe data and the calculated Ni distribution curve can then be made and the comparison used to determine whether one unique set of conditions exists for the growth of the kamacite plate. The parametric method of analysis can be extended for usc in other —y areas in the same meteorite and for use in areas in more than one meteorite. It can also be used to determine the validity of the different cooling models proposed. Four values of B and AT, which give a calculated kamacite bandwidth the same size as that for Area 1 in the Carlton meteorite (Fig. 11), were determined (Model 1).
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The concentration gradients cal The kamacite band is 75 wide, and X0 culated for the four different-sized bodies by means of the growth analysis are shown in Fig. 15. It is apparent that the 100 km body does not give the correct concentra tion gradient in taenite. A good fit is, however, obtained for B = 250, 500, and $00 km. It appears that for cooling Model 1 no unique radius for the parent mete orite body exists. We confirmed this conclusion by a similar analysis for the —y areas in the Dayton meteorite. We should note, however, that according to this model, the maximum allowable pressure was 12 kb. .
I•0
08
O6
8 :04
O2
0 0
O2
04
06
08
1•0
wxo/ xo Fig. 14. Effect of X0 on the width of the kamacite band.
The parametric technique was also used to determine the combinations of B and 1T for this same area in the Canton meteorite for Model 2. The calculated con centration gradients for B = 100, 200 and 500 km are plotted in Fig. 16. For this cooling model a unique fit of concentration versus distance is obtained at B = 200 km. To test this solution (B = 200 krn), we calculated G vs. X in the taenite phase for Areas 1, 2 and 3 in the Carlton meteorite. The calculated curves are shown in Fig. 17. The agreement is very close. Note that as the amount of undercooling decreases, the value of 1V increases. Also, the calculated concentration distribution curves above 30% Ni are unaffected by the amount of undercooling. If a unique radius of 200 kin exists for the parent meteorite body, then the con centration distribution curves calculated by this model for meteorites other than the Carlton should agree with measured probe data from those meteorites. The growth analysis was applied to three different meteorites, Canyon Diablo, Carlton and Dayton. The Canyon Diablo scan had already been measured (GoLDsTEIN, 1962), and the distance scale was adjusted so that the scan was taken perpendicular to the /y interface. The results of the calculations are shown in Fig. 1$. The measured and calculated distribution curves fit very closely. The analysis shows that the Widman stätten pattern in meteorites, from the coarsest octahednites to the finest ataxites, could have been formed from one or several parent bodies at low pressures. We have also investigated cooling Model 4. Of particular interest here are bodies whose internal pressures are high, 25 and 40 kb. Even if no undercooling occurs
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J. I. GOLDSTEIN and R. E. OGILvIE
914
before precipitation, the maximum bandwidth is calculated to be 3 jc at 40 kb, and 32 at 25 kb for the Carlton meteorite. Most of the measured values of JV in the Canton are over 100 t. Internal pressures of this order of magnitude are therefore not reasonable under any conditions. The two measured inputs for the growth analysis were the Fe—Ni phase diagram 50
45 MODEL#I CARLTON METEORITE W— 75±
40 H ci
z 0
R° a R° V R R=
35
100 km, AT 55°C 250 km, AT = 115°C 500 km, AT ° 25°C, P=4kb 800 ka, AT = 90°C, P ° 10kb
H
z LU
C
z
0
C -J LU C
25
z
.
20 sured Curve
I5
DISTANCE IN MICRONS
Fig. 15. Calculated and measured composition distribution curves in taenite, Model 1.
and the Fe—Ni interdiffusion coefficients. The growth analysis was tested to see what effect the errors in the determination of C+1 and D had on the calculated values of flT A systematic error in G’ of +05 i\t% or about 5°C in the nucleation tem perature yields an uncertainty in W of only 6 per cent. A systematic error in G+ of + P0 At % or about +10°C in the nucleation temperature yields an uncertainty in TV of only 14 per cent. An uncertainty of +25 per cent in the extrapolated dif fusion coefficients yields an uncertainty of 10 per cent in TTT; of +50 per cent, an uncertainty of 20 per cent in W. These errors are small. They affect the resultant °Ni vs. X The extrapolated 13 values from an early diffusion study of the Fe—Ni system (WELLs and MEJa, 1941) were also used in order to see what effect they had on the calculated values of TV. The Wells and Mehl values of D had the effect of increasing TV by over 300 per cent. curves
to
a
much
smaller
degree
than the
errors
in
I
TV predict.
.
Authors Copy
The growth of the Widmanstatten pattern in metallic meteorites
915
DISCUSSION
We have used the growth analysis to determine the Ni distribution in taenite and to determine the kamacite bandwidths in metallic meteorites. The results of the growth analysis were compared with the measured Ni distribution in taenite from electron-probe microanalysis. We have also determined the effect of the variables that influence the growth process. The errors in the mcasurement of the interdiffusion 50
45
40 H 2 0
35
or H 2
w
U 2 0 U -J U
30
sr 25
U 2
20
IS
DISTANCE IN MICRONS
Fig. 16. Calculated
and measured composition distribution curves in taenite, Model 2.
coefficient, the Fe—Ni phase diagram, and the error resulting from variation of ther mal diffnsivity a with temperature cause only a small error in the growth analysis. Several conclusions can be drawn from the results of this work about the forma tion of the Widmanstatten pattern in metallic meteorites. The value of the Ni con centration in taenite at the a/p boundary has not been measured very accurately with the electron probe. The values reported to date lie between 35 and 45% Ni, depending on the investigator and the electron-probe used. The growth analysis shows that a steep Ni gradient exists in the taenite near the a/p boundary. In fact, the calculated Ni concentration varies from 35 to 50 per cent within the first micron of the taenite phase. Since the X-ray resolution of the electron probe is at best one
Authors Copy
J. I. GOLDSTEIN and R. E. OGILvIE
916
micron, only an average value of G should be expected at the /y boundary. There fore the Ni concentration in taenite at the o/y boundary is probably close to 50 per cent. The Ni conceiltration in kamacite is uniform, except near the c/y boundary, where a decrease of up to 1 per cent is observed (AGRELL, LoNG and OGILvIE, 1963). Several 50
45
40
z
MODEL #2 CARLTON METEORITE RADIUS= 200 km
35
• Area I, W 75, AT l20°C,W/X o o Area 2,W 90u, AT Il0°C,W/X0049 Area 3,Wo l25, AT o95°C, W/X,044
0
H
z 30 w U z 0
U
-J
w 25
.
U
z 20 Curves Meteorite
I0 5,tu
DISTANCE IN MICRONS t104cm)
Fig. 17. Calculated and measured composition curves in taenite in 3 areas, Model 2.
theories have been proposed to explain the decrease. The simplest of these involves the bending back of the + y boundary of the one-atmosphere phase diagram at low temperatures. As the meteorite cools below 400°C, the value of the Ni content in the phase at the cd/y boundary will decrease. This causes the taenite to begin to grow with respect to the kamacite. Because nickel is rejected from the phase and D5 is no longer infinite, a gradient of Ni will develop at the border of the /y interface. Unfortunately, the Fe—Ni diagram is not accurately known below 500°C. An analysis of the X-ray data (OWEN and Liu, 1949; OWEN and SULLY, 1939) taken below 500°C indicates, however, that the o’./ + y boundary probably bends back at about 400°C. Therefore the Ni concentration of the and y phases at the interface indicate a final growth temperature of about 350°C at low pressures.
4
.
Authors Copy
The growth of the WTidmanstdtten pattern in metallic meteorites
917
That no Widmanstatten pattern is present in meteorites containing more than 13 wt% Ni has led Firno (1954) to postulate that pressure was the factor that pre vented its formation. Uhlig argues that pressure serves to lower the transformation phase will precipitate at temperatures where temperature, y n + y, so that the the diffusion of Ni in taenite is insufficient to allow the Widmanstatten structure to —÷
form (
