The cooling rates of iron meteorites—A new approach

ICARUS 45, 564-576 (1981)

The Cooling Rates of Iron Meteorites--A New Approach K. L. RASMUSSEN Physics Laboratory 1, H. C. Oersted Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark Received December 12, 1979; revised October 22, 1980 Measurements of Ni concentration profiles of a large number of neighboring kamacite and taenite lamellae in the iron meteorite Cape York (IliA) have revealed that the kamacite plates have nucleated in a taenite of varying Ni concentration, equal to or above the bulk Ni concentration of the meteorite. This variation indicates that the kamacite plates nucleated stepwise (i.e., independently) during cooling through a certain temperature interval, rather than simultaneously after more or less undercooling of the meteorite. The latter is assumed in most previous cooling rate determinations (e.g., Moren and Goldstein, 1978). In this paper the measured local bulk Ni concentrations are used in the computer simulation of the evolution of the Widmannstaetten pattern in order to calculate the cooling rate of the meteorite. The cooling rate obtained for Cape York is 1.3 °K/my. In most previous work, a correlation is seen between the resulting taenite width and the cooling rate in one and the same meteorite. No such correlation is seen using the present method. 1. INTRODUCTION

Wood (1964)and Goldstein and Ogilvie (1965b) describe a way to obtain the metal-lographic cooling rates of octahedrites. Since the publication of these papers, progress has been made along several different lines. The F e - N i - P phase diagram has been revised by Willis and Wasson (1978) and Moren and Goldstein (1978), and recently by Romig and Goldstein (1980). The diffusion coefficients of Ni in taenite and kamacite were reported by Goldstein et al. (1965a), and have been revised by Heyward and Goldstein (1973). There are two obvious problems in the previously published papers on cooling rate determinations. Firstly, in most papers it was assumed that an undercooling was necessary if one wanted to simulate all measured lamellae. It seems that an undercooling of at least 100°K is necessary for the coarse and medium octahedrites, and for the broad lamellae in group IVA iron meteorites (Moren and Goldstein, 1978). Undercoolings of up to 190°K have been reported (Moren and Goldstein, 1978). Such large undercoolings seem implausible.

The second problem of the classical method is the tendency for the measured taenite lamella width to be correlated with the cooling rate. Published examples are numerous (e.g., Wood, 1964; Moren and Goldstein, 1978; Willis and Wasson, 1978; and Figs. 11 and 12 of this paper). The explanation proposed by Moren and Goldstein (1978) and Willis and Wasson (1978) for this is that the wide taenite lamellae were formed in areas which suffered the largest undercooling. This explanation is not confirmed by the present study. Essentially the cooling simulation procedure has been unaltered since Wood (1964). The present paper describes a cooling simulation with an additional input parameter, the measured local bulk Ni concentration in the taenite just before kamacite nucleation. This invention solves both problems mentioned above. 2. LOCAL BULK-Ni-CONCENTRATION VARIATIONS IN CAPE YORK

Cape York (IIIA) has been chosen for this study. Cape York is a typical member of group IIIA, which is the largest group of iron meteorites. Its metallographic struc564

0019-1035/81/030564-13502.00/0 Copyright© 1981by AcademicPress, Inc. All rightsof reproductionin any formreserved.

COOLING RATES--A NEW APPROACH ture has b e e n described by Buchwald (1975). 2.1. The m e a s u r e m e n t s w e r e carried out on the Cambridge 180 Scanning Electron M i c r o s c o p e at the L a b o r a t o r y of Micropaleontology, University of Copenhagen. The instrument was operated with a primary acceleration voltage of 15 kV, as this gives the best resolution (least penetration and smallest reaction zone) and also allows for u n m a s k e d Fe- and N i K a lines. The b e a m current was a b o u t 250 /xA. A K e v e x Si(Li) solid state detector was used as a detection system. A present lifetime of 10 sec was used for profiling points across taenite lamellae. A preset m a x count of 5000 counts per 10 eV in the m a x i m u m point of the FeKct line was used for midprofile concentrations, standards, and kamacite m e a s u r e m e n t s . Tests and statistics on the reproducibility and stability of the entire s y s t e m were c a r d e d out several times. It turns out that the spatial resolution in the "infinitely" thick F e N i samples is better than 0.8/.,m. To eliminate possible misalignments in the shown and the real position of the spot, micrographs were always taken of the b u r n m a r k s , and the geometrical m e a s u r e m e n t s were p e r f o r m e d on these. 2.2. The F e N i standards were synthesized b y melting the appropriate a m o u n t s of analytical grade F e and Ni in an inert ,,

a t m o s p h e r e , followed b y annealing. T h e s e standards were cut and subsequently polished down to 1-/~m diamond finish, just like the meteorite. Standards of 8.38, 25.95, 36.15, and 46.24 w t % Ni were used. Standards were m e a s u r e d twice each day to monitor drift. F o r the taenite, a straight line was fitted to the standard m e a s u r e m e n t s and used as calibration. F o r the kamacite, the 8.38 w t % Ni standard was used only. The sample-detector and the standard-detector g e o m e t r y were kept identical in order to eliminate matrix corrections. Statistics on the reproducibility of the m e a s u r e m e n t s show that the a c c u r a c y in Ni-concentration determination is better than 0.5% Ni (one standard deviation). 2.3. In the present study, 46 taenite lamellae and their environments were studied. T h e s e 46 lamellae w e r e selected only after the criterion that each lamella should be long and straight, and sandwiched bet w e e n two parallel tae~fite lamellae, with kamacite bands in b e t w e e n (see Fig. 1). The total widths of the lamellae, the midprofile concentrations, and the local bulk Ni concentrations were m e a s u r e d for all 46 lamellae. (These quantities are hereafter referred to as TW, MPC, and BLK.) TW varied from 4.8 to 85.8 /zm. The B L K values were determined as the a v e r a g e Ni content of the close environments of the individual lamellae, obtained b y using area scan on the

Xo(lJ

=4~_

I

d

Xo(3)

=

j

I

' I I i

I i

2O

i

565

11

I

I i i

I

v

/~00 Distance,

I I i I

@

~.f microns

1000

I3

~5' X=~(.1,)

FIG. l. The Ni concentration as a function of distance over a polished surface of the meteorite. I 1, 12, and I3 are the integrals (the shaded areas) of the taenite lamellae, measured in microns times wt% Ni. The lamella under study is the one labeled 2. The distances X,(I) and X,(3) are measured from midpoint to midpoint in the taenite lameUae. The distances Xo(1) and X0(3) are the start dimensions of the taenite before kamacite nucleation, i.e., indicating the kamacite nucleation sites.

566

K. L. RASMUSSEN

FIGS. 2-5. Typical regions showing Ni-enriched fields o f t a e n i t e lameUae. The very broad kamacite lamellae (A) just outside the taenite fields are those nucleated very early, possibly without a n y undercooling at all. The areas of B L K m e a s u r e m e n t s are indicated, and the Ni wt% is written beneath them. Note that all areas are enriched in Ni relative to the content of the whole meteorite: 7.84 w t % Ni.

COOLING RATES--A NEW APPROACH

Imm I

......

FIGS. 2-5--Continued.

567

568

K. L. RASMUSSEN

kamacite, and closely spaced profiling points on the taenite. The parts of the kamacite to be included in this area scan are the parts between the original nucleation sites. The nucleation sites are found from the following equations (see Fig. 1): X0(I) = X~,(I).I2/(ll + •2); )(o(3) = X~(3)-12/(12 + •3). Note that this assignment gives a B L K value which is slightly lower than the value obtained by measuring the Ni content between the midpoints of the neighboring kamacite bands. The B L K value is checked against area scans on the whole area (including the taenite lamellae itself), and it is found that it does in fact reflect the mean Ni content of the area under consideration. This procedure, which might seem a little complicated, is applied to secure easy reproducibility of the measurements. As a first approximation, the local bulk Ni concentration is assumed to be constant over the taenite between the two kamacite nucleation sites, before kamacite nucleation. Examples of fields having local bulk Ni enrichments are shown in Figs. 2-5. Areas of the local bulk-Ni-concentration measurements are indicated. Beneath each area is written the bulk Ni concentration in weight percent Ni. It is clearly seen that the Ni contents of these areas are elevated relative to the 7.84 wt% Ni, which is the wholemeteorite bulk value of Cape York (Buchwald, 1975). The delay in nucleation temperature given by a B L K value is found from the taenite/taenite-kamacite curve in the phase diagram. This delay, measured in degrees Kelvin, is called DT. The transformation between B L K and D T is practically linear. The distribution of the DTs is shown in Fig. 6.

3. THE REVISED COOLING SIMULATION MODEL

In the old method it is assumed that all kamacite nucleated simultaneously (as stepwise nucleation inevitably would create

local bulk Ni variations in the taenite). Comparing calculated values of T W and M P C with measurements, one is forced to introduce the concept of undercooling to explain the discrepancy between measurements and theory. As local bulk Ni variations were shown to exist above, we are forced to leave the old model and devise a new one which is in accordance with the measurements. A new model is proposed then. It has a different scenario than the old model, namely, the following: At least a few kamacite lamellae nucleate very close to the highest possible nucleation temperature (i.e., the temperature given by the F e - N i - P phase diagram for the bulk Ni and P values of the meteorite). After this initial nucleation, the remaining taenite is rapidly enriched in Ni, creating the local bulk Ni enrichment as measured. As temperature falls, more kamacite lamellae nucleate, now in environments somewhat higher in Ni content than the early ones. As diffusion is swift at these elevated temperatures, only moderate gradients will build up during this enrichment. In short only a slight undercooling is necessary; what is needed is a rather short interval of kamacite nucleation times. To justify this interpretation of the measured local bulk Ni enrichment, the diffusion length--which is the square root of the diffusion coefficient multiplied by the time--can be calculated to be approximately 7 mm; when the temperature is 1050°K, the time span 30 my, and the Ni content 7.84 wt% (Goldstein et al., 1965a). Let us turn to the precise definition of the cooling simulation. The details of the classical cooling simulation method is described in Wood (1964), Goldstein and Ogilvie (1965c), and Willis and Wasson (1978). The points of interest here are the basic assumptions and procedures of the classical method: 1. Diffusion is assumed to be one dimensional and to obey Fick's law at all temperatures, both in taenite and kamacite.

COOLING RATES--A NEW APPROACH

569

DT--DIS~IBUTION •

1

i

I

I

1, HI]HI]. I

2O

80 ffl',K

FIG. 6, The distribution of DT. D T is the delay in nucleation relative to the highest possible nucleation temperature. D T is measured in °K, and is found from the y/(3~ + a) curve in the phase diagram by means of the measured B L K value.

2. The taenite lamella is grown from both sides simultaneously. 3. The distance between kamacite nucleation sites is varied to yield all values of the width of the resulting taenite lamella. 4. The Ni concentration in the taenite just before kamacite nucleation is taken to be the bulk Ni concentration of the whole meteorite. 5. Thermodynamic equilibrium is assumed at the o~/y interface at all times. The effect of P is included in the phase diagram. 6. The only parameter is the cooling rate (hereafter called the CR). Either a linear or an exponential cooling history can be applied. 7. The measurements are the T W and the M P C of the taenite lamella. 8. The result of the calculation can be represented in a diagram: M P C against TW. In this diagram, curves of constant CR can

be drawn for a series of different cooling rates. In the same diagram all measured lamellae can be plotted as points. In order to take the measured local bulk Ni variations into account, the new simulation model is based on the following eight assumptions and procedures: 1. Diffusion is assumed to be one dimensional and to obey Fick's law at all temperatures, both in taenite and kamacite. 2. The taenite lamella is grown from both sides simultaneously. 3. The distance between kamacite nucleation sites is varied to yield all values of the width of the resulting taenite lamella. 4. The Ni concentration in the taenite just before kamacite nucleation is taken to be the measured local bulk Ni concentration at the site of the lamella under consideration, and it is assumed to be constant.

570

K. L. RASMUSSEN

5. T h e r m o d y n a m i c equilibrium is assumed at the a / y interface at all times. The effect of P is included in the phase diagram. 6. The only p a r a m e t e r is CR. In principle, any single-parametric cooling history can be applied. In this work, I have a s s u m e d a linear cooling history, in the interval 800 to 400°C. 7. The m e a s u r e m e n t s are the T W and the M P C of the taenite lamella, and the local bulk Ni concentration of the e n v i r o n m e n t s (BLK). 8. The result of the calculation can be represented in a series of diagrams showing M P C against TW, each having a different B L K value. This is to say: each diagram has a different bulk Ni value at the start of the simulation.

B L K values of 0. l w t % Ni. One of the plots is shown as an example in Fig. 7. Undercoolings were set to zero in all these calculations. N o t e that I have preferred not to take the logarithm of the width in order not to m a s k the d i s c r e p a n c y b e t w e e n measurements and theory at large TW. A resolution of 50 points in the taenite and 50 points in the kamacite was used in the c o m p u t e r simulations. The resulting distribution of CRs is shown in Fig. 8. The corresponding mean and standard deviation is 1.28 + 0.55°K/my. S o m e of the spread in cooling rate originates from unfulfilled premises (e.g., the planar growth can be disturbed by, for instance, a nearby Schreibercite crystal, now invisible because it is just a b o v e or just below the surface). Some of the spread in CR also originates from the error in M P C determination. An uncertainty of 0.5 w t % Ni in M P C will give an

In the present study, c o m p u t e r calculations were p e r f o r m e d with a spacing in N[=8.75

P=0.15 U=O i

MPC pc.

48

~O

20

••0.5 I

I 40

i ~

I 88

K/my 1.0 1.5 20 3.0 5.0

I TOO

TW

I 120 y

FIG. 7. MPC as a function of TW. The bulk Ni content of this particular plot is set to 8.75 wt%. The P content is set to 0.15 wt% (Buchwald, 1975). The curves are the computer simulations, with the CR written close to them. The points are the measurements with measured BLK values close to 8.75. Twenty-one other diagrams of this type have been made with different BLK values in the present study. _,,

~Ib'TRISLFI~ F

Y

T

T

T

0

1

2

5

4

0 CR

5

FiG. 8. The distribution of the cooling rates obtained from the new method. The C R s are measured in degrees Kelvin per million years. Forty-six lamellae have been used in the present study. The mean is found to be 1.28°K/my, and the standard deviation is 0.55°K/my.

CR = 0.6 K/my ~ x.BLK = 7.84 w't % N ~ +

+++++.',,..

,J

/+++4-

4-

CR=/..0 K/my 8LK = 7,84 wt%Ni

/ I

~

20

i

I

! , ~ +

I

I

+ + K-

0

I

I

I

I

I

2o ~

i

FIG. 9. The computer curve fit (solid line) and the measurements (crosses) of the taenite Ni concentration profile, using the old method. The three lamellae are drawn to the same scale, and selected only after their width. ~71

CR = 1.B K/my BLK = g.05 w t % Ni

CR= 1.1 K/my j

+÷.~

8LK= 10.62 wt % Ni

÷

S I

l

I

I

I

I

60

CR=1.2 K/my BLK= 9.39 wt */, Ni

I

20

I

I

;

;

~ -.

20,u .

---.-__._. I

I

I

I

I

I

FIG. 10. The same three lamellae as on Fig. 9, but now the c u r v e fit is p r o d u c e d using the ne w method. The m e a s u r e d B L K values are indicated. ~-YI:I~K

N178t+ 1:~.15 UO. I

I

I

I

I

I

MPC pc

30

-q-

+

20

~

+

+4"++ 4-

÷

~

+4-

+ ++

~

0.5 K/my 1.0 5.O

I0

I

I

I

I

I

20

~

60

88

100

I

TW

120 u

Fze. 11. M P C as a function of TW. The bulk Ni contest is set to 7.84 w t % , and the P c ont e nt to 0.15 w t % , as cited by B u c h w a l d (1975). The undercooling is set to zero. This diagram c ons t i t ut e s the o u t c o m e of the old method. As can be seen, the m e a s u r e m e n t s are d i s c o r d a n t w i t h the computersimulated curves. 572

COOLING RATES--A NEW APPROACH uncertainty of about 0 . 2 ° K / m y for a cooling rate of around 1.3°K/my, and a T W of around 50/zm. In Fig. 9, three e x a m p l e s of the c u r v e fit to the taenite Ni concentration profiles are shown, using the old method. In Fig. 10 the s a m e is s h o w n using the new method. It is clear that the new method gives a substantially better c u r v e fit, especially for the wider lamellae.

lameUae systematically gives the lowest cooling rates. As all lamellae have experienced the same cooling history, this result is v e r y dissatisfying. I f one chooses the lamellae with T W b e t w e e n 50 and 100/zm, an unrealistically low CR would result. In contrast to Figs. 11 and 12, it can be seen in Figs. 15 and 7 that the new m e t h o d , which takes the local bulk Ni variations into consideration, shows no correlation b e t w e e n T W and CR. Therefore, in m y view, Figs. 11 and 12 show the insufficiency of the old method in the case of a typical g r o u p - I l i A iron, and Fig. 15 shows the efficiency of the new m e t h o d on the same meteorite. H o w ever, the new a p p r o a c h offers an, at least, equally good alternative to the old scenario of simultaneous kamacite nucleation, besides it explains the m e a s u r e d local bulk Ni enrichments. One could speculate whether or not there exists a relationship b e t w e e n the new pa-

4. DISCUSSION Figure 11 shows the T W - M P C diagram for the established 7.84 w t % Ni of Cape Y o r k , assuming simultaneous nucleation of the kamacite and no undercooling. In Fig. 12 the s a m e is shown, except that the undercooling is set to 100°K. These diagrams show the o u t c o m e of the classical method. Both in Fig. I 1 and in Fig. 12, it is clear that there is a correlation b e t w e e n CR and TW, in the sense that the b r o a d e s t CAPE-YORK Ni"~it,,. i

573

PO.15 UlOO.

MPC pc

40

~0

41-

÷

÷ ÷ ÷~÷

4-

4-

÷ ÷÷

÷+ ÷

÷+

÷

÷

20

0707 ,

/,,O

60

80

IO0

I

TW

120 y

FIG. 12. MPC as a function of TW. Bulk Ni content is again set to 7.84 wt%, the undercooling is now set to 100°K. This diagram constitutes the outcome of the old method with undercooling included. It is obvious that the measurements are discordant with the theoretical curves.

R-Or-PLOT .

.

.

.

I

.

.

.

.

I

.

.

.

.

I

DT K

80 ---t---ta]

---I-----t-

"-t-

++ I

--I--

0

,

,

,

,

I

.

.

I

.

+

+

,I,-1--

.

I

1

,

,

,

,

I

5

2

CR

K/my

FIG. 13. D T plotted against CR for the n e w m e t h o d . N o relationship e m e r g e s from this diagram; it rather looks as if D T is uncorrelated with CR.

114-1~r--PLOT DT K

4-

6O 4-

4-

444-

÷ ÷

+ 4-

2O

,I-4÷

+÷

4-

÷÷ +

4-

4-

44-

4-

÷

4-

÷

o

÷ 4-

44.

1~" 4-

+ 4-

+

÷

÷

.~4-

4-

4÷

I

I

I

4O

60

I

TW

80

).J

FIG 14. D T plotted against T W for the n e w m e t h o d . It s e e m s that no correlation exists b e t w e e n D I and TW. 574

COOLING RATES--A NEW APPROACH

575

~-%/--~0]" .

.

.

.

I

.

.

.

.

I

.

.

.

.

I

TW

P

--I---I-

--t-

--t-

---I--

---I--

--I--

_.i_ --I----II

--tTI--~ --I--

LI

"--I---~ ---I-0

,

,

...i._ ~ " --I--

--I-,

,

I

,

,

,

,

I

.

.

.

.

I

FIG. 15. CR plotted against T W for the new method. It seems that CR is uncorrelated with TW. This

is of major importance, since the opposite would indicate violation of some of the assumptions on which the calculations are based. rameter B L K , or equivalently DT, and one or more of the other parameters. It would be rather bad if there were a correlation between CR and DT, whereas a correlation between D T and, for instance, T W would be quite acceptable. In Fig. 13, D T is plotted against CR, and no correlation is seen. This is another important observation justifying the new method. In Fig. 14, D T is plotted against TW, and again no correlation appears. 5. C O N C L U S I O N

A new method is proposed for the simulation of the growth of the Widmannstatten pattern in octahedrites. It involves a new parameter, the measured local bulk Ni concentration at the time of kamacite nucleation, reflecting a delay in the nucleation of some o f the kamacite lamellae, relative to the earliest possible nucleation. With this model, the cooling rate of Cape York turns

out to be 1.28 _+ 0 . 5 Y K / m y . N o correlation exists between CR and T W for the new method as it does for the old method. The delay in kamacite nucleation in this study of Cape York is found to vary from 4 to 71°K, corresponding to time spans from 5 to 91 my. It is concluded that the old method is unable to simulate the growth of the Widmannstaetten pattern properly in Cape York (IIIA), whereas the new method does so quite sufficiently. ACKNOWLEDGMENTS I wish to thank J. F. Albertsen for very useful discussions, and H. J. Hansen and the Geological Central Institute for permission to use the Scanning Electron Microscope. Thanks also to the RC4000

Computer Department at H. C. Oersted Institute for putting their machine at my disposal, and to V. F. Buchwald, who has supplied the sample for this study. REFERENCES BUCHWALD,V. F. (1975). Handbook oflron Meteorites. Univ. of California Press, Berkeley.

576

K. L. R A S M U S S E N

GOLDSTEIN, J. I., HANNEMAN, R. E., AND OGILVIE, R. E. (1965a). Diffusion in the Fe-Ni system at I atm and 40 kbar pressure. Trans. Met. Soc. A I M E 233, 812-820. GOLDSTEIN, J. I., AND OGILVIE, R. E. (1965b). A reevaluation of the iron-rich portion of the F e Ni system. Trans. Met. Soc. A I M E 233, 20832087. GOLDSTEIN, J. I., AND OGILVIE, R. E. (1965c). The growth of the Widmanstaetten pattern in metallic meteorites. Geochim. Cosmochim. Acta 29, 893920. GOLDSTEIN, J. I., AND SHORT, J. M. (1967). The iron meteorites, their thermal history and parent bodies. Geochim. C o s m o c h i m . Acta 31, 1733-1770. GOLDSTEIN, J. I. (1969). The classification of iron meteorites. In Meteorite Research (P. M. Millman, Ed.), Symposium Vienna, 1968, Reidel, Dordrecht. HEYWARD, T. R., AND GOLDSTEIN, J. I. (1973).

Ternary diffusion in the alpha and gamma phases of the FeNiP system. Metal. Trans. 4, 2335-2342. MOREN, A. E., AND GOLDSTEIN, J. I. (1978). Cooling rate variations of group IVA iron meteorites. Earth Planet. Sci. Lett. 40, 151-161. ROMIG, A., AND GOLDSTEIN, J. I. (1980). Determination of the Fe-Ni and the Fe-Ni-P phase diagrams at low temperatures (700-300°C). Metal. Trans. l l A , 1151-1159. WILLlS, J., AND WASSON,J. T. (1978). Cooling rates of group IVA iron meteorites. Earth Planet. Sci. Lett. 40, 141-150. WOOD, J. A. (1964). The cooling rates and parent planets of several iron meteorites. Icarus 3, 429459. WOOD, J. A. (1979). Review of the metallographic coolingrates of meteorites and a new model for the planetesimals in which they formed. In Asteroids (T. Gehrels, Ed.), Univ. of Arizona Press, Tucson.