Available online at www.sciencedirect.com
Geochimica et Cosmochimica Acta 105 (2013) 206–220
www.elsevier.com/locate/gca
H-chondrite parent asteroid: A multistage cooling,
fragmentation and re-accretion history constrained by
thermometric studies, diffusion kinetic modeling
and geochronological data
Jibamitra Ganguly a,⇑, Massimiliano Tirone b, Sumit Chakraborty b,
Kenneth Domanik c
b
a
Department of Geosciences, University of Arizona, Tucson, AZ 85721, USA
Institut für Geologie, Mineralogie und Geophysik, Rühr-Universität, D-44780 Bochum, Germany
c
Lunar and Planetary Laboratory, University of Arizona, Tucson, AZ 85721, USA
Received 2 March 2012; accepted in revised form 15 November 2012; Available online 5 December 2012
Abstract
We present a detailed thermometric study and cooling history analysis of selected H-chondrites from the petrologic types
4–6 on the basis of their mineralogical properties, and integrate these data with other available constraints on the cooling rates
to develop a comprehensive model for the cooling, fragmentation and re-accretion history of the parent asteroid. Temperatures have been determined on the basis of two-pyroxene (2-Px) and spinel (Spnl)–orthopyroxene (Opx)/olivine (Ol) thermometers using the average of line scans and distributed spot analysis of coexisting pairs in each set. All of these minerals have
been found to be compositionally homogeneous from 1 to 2 lm from the interface within the resolution of microprobe analysis. The thermometric results for the H5 (Allegan and Richardton) and H6 (Guarena and Kernouvé) samples are very similar. Also, while the 2-Px temperature increases by 90 °C from H4 to H5/6, a reverse trend is observed for the Spnl–Opx/Ol
temperatures implying compositional resetting of these pairs during cooling. For the H4 sample (Forest Vale) all thermometric results are similar. The cooling rates calculated from numerical modeling of the compositional profiles in Opx–Cpx pairs in
H5 and H6, corrected for the spatial averaging or convolution effect in microprobe analysis, are 25–100 °C/ky, which are 3–
4 orders of magnitude higher than the cooling rates implied by in situ cooling in an onion-shell parent body model. Similar
numerical simulation of the compositional profile in Opx–Spnl pair in H4 yields a cooling rate 50 °C/ky, which is in very
good agreement with recent metallographic cooling rate of this sample and geochronological constraints on the cooling T–t
path. Numerical simulation suggests that the slow cooling of the H5/6 samples at a rate of 15 °C/My, as deduced by recent
metallographic study, could not have commenced at a temperature above 700 °C since, otherwise, the simulated compositional profile fails to match the observed profile. For the H5 samples, the T–t path constructed on the basis of Hf–W age of
peak metamorphism and two stage cooling model satisfies the constraints imposed by the Pb–Pb ages of the phosphates and
Ar–Ar ages of the feldspars vs. their respective closure temperatures, whereas that for H6 samples constructed using the same
approach fails to satisfy these geochronological data. A second stage of even slower cooling at 3 °C/My needs to be invoked
to satisfy the geochronological age vs. closure temperature relations. We present a model of fragmentation and re-accretion
history of the parent body that could lead to the reconstructed T–t paths of the H-chondrite samples studied in this work, and
discuss some of their broader implications. The cooling rates retrieved from the available data on the Fe–Mg ordering states
of orthopyroxenes of some other H5 and H6 samples are orders of magnitude faster than the metallographic cooling rates that
⇑ Corresponding author.
E-mail address: ganguly@email.arizona.edu (J. Ganguly).
0016-7037/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved.
http://dx.doi.org/10.1016/j.gca.2012.11.024
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
207
are applicable to similar low temperature domain. It is, thus, likely that all samples of the same petrologic type did not share a
common cooling history.
Ó 2012 Elsevier Ltd. All rights reserved.
1. INTRODUCTION
Known falls of chondritic meteorites, which are generally accepted to be very primitive and undifferentiated objects of the solar system, are grouped into three chemical
classes, carbonaceous, ordinary and enstatite chondrites.
On the basis of their iron and metal contents, the ordinary
chondrites are further subdivided into three chemical classes, H, L and LL, and petrologic types 3, 4, 5 and 6,
depending on the intensity of metamorphism and textural
maturity that increase in the above sequence (e.g. Wasson,
1985). It has been argued that since they share common
properties, such as oxygen isotope composition, oxidation
state and major element chemistry, the samples of a given
chemical group were derived from a specific parent asteroid
(Wasson, 1985; Trieloff et al., 2003).
The structure and cooling history of H-chondrites have
been subjects of considerable debate for many years (Taylor
et al., 1987; Lipschutz et al., 1989; Ganguly and Tirone,
2001; Trieloff et al., 2003; Kessel et al., 2007). Recently,
however, the so-called “onion shell” model, in which the
progressively higher petrologic types were supposed to have
been buried at increasing depths (Fig. 1), seems to have
gained greater acceptance in the planetary science community, especially after two detailed thermochronometric studies (Trieloff et al., 2003; Kleine et al., 2008) of the different
petrologic types of H-chondrites. These studies showed that
the closure temperature (Tc) vs. age data of the metamorphic types 4–6 by several geochronological methods fall
on the cooling paths calculated for different depths in a
parent asteroid of 50–100 km radius that was heated by
the decay of 26Al(26Al ! 26Mg + b) and cooled by heat
conduction (Fig. 1) (Trieloff et al., 2003; Kleine et al., 2008).
On the basis of mineralogical data, Kessel et al. (2007)
recently suggested that the cooling rate of H6 chondrites
could be considerably higher than that suggested by the
thermochronological data. Their conclusion is based on
modeling the extent of resetting of temperature derived
from olivine (Ol)–spinel (Spnl) Fe–Mg exchange thermometer of Sack and Ghiorso (1991a,b) relative to earlier data
(Bunch and Olsen, 1974) on temperatures obtained from
empirical calibration of orthopyroxene (Opx)–clinopyroxene (Cpx) “solvus thermometry”. The high temperature
cooling rates could be constrained by modeling diffusion induced compositional zoning near the interface of mineral
pairs (olivine–spinel, orthopyroxene–spinel/clinopyroxene)
and such compositional zonings are also expected in the
higher petrologic types if these have indeed cooled as slowly
as deduced in the earlier studies (Trieloff et al., 2003; Kleine
et al., 2008). However, this expectation is not compatible
with the few compositional profiles shown by Kessel et al.
(2007) that show almost uniform mineral compositions as
function of distance from the interface of olivine–spinel
pairs. Furthermore, on the basis of their study on the Fe–
Mg ordering states of orthopyroxenes, Folco et al. (1996)
concluded that the petrologic types 4–6 of H-chondrites
had cooled in similar environments in the low temperature
regime as they have similar cation ordering states reflecting
(ordering) closure temperatures of 400–500 °C that have
no correlation with the petrologic types. This observation
H4
H-3
H5
H6
Fig. 1. (a) Temperature–time paths at different radial distances in a supposed spherical parent body of H-chondrite of 100 km radius and
heated internally by 26Al decay, as calculated by Kleine et al. (2008), and comparison with the age vs. conventional closure temperature data
of H-chondrites of different petrologic types (H4, H5 and H6) according to several decay systems. (b) A conceptual layered parent body model
of H-chondrites that seems to be compatible with the thermochronological data and T–t histories at different radial distances in the parent
body.
208
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
orthopyroxene–spinel (Opx–Spnl) and olivine–spinel (Ol–
Spnl). We have analyzed a number of these coexisting pairs
as well as isolated grains. The conditions of the microprobe
analyses are as follows: 20 kv accelerating voltage, 20 nA
beam current with a focussed beam of 1 lm diameter,
20 s counts on the peak and 20 s on the background. Most
of the microprobe analyses were carried out in two Cameca
SX-50 models. (All microprobe data could be made available upon request to the senior author.)
Regardless of the meteorite sample, grain size or coexisting phase, every grain of olivine, clinopyroxene, orthopyroxene and spinel that we have analyzed was found to be
almost homogeneous in composition within the resolution
of microprobe analysis. Several representative compositional profiles from the three petrologic types, H4, H5
and H6, are illustrated in Fig. 2, with the data for Mg#
in enlarged scales. The spinel grains in all samples were
found to be very chromium rich (X(Cr) 0.80–0.85). Clinopyroxenes (Cpx) grains are very small (a few tens of microns or less) and as a consequence we have not been able
to detect them optically. However, we succeeded in detecting these grains on the basis of Ca X-ray maps in an electron microprobe.
Detailed examination of BSE images of a thin section of
Richardton in Cameca-SX100 suggests a reaction relation
between orthopyroxene and a groundmas of alkali rich plagioclase composition to form clinopyroxene. The SX-100
also seems to be incompatible with the onion-shell parent
body model and in situ cooling of the samples that is expected to produce an inverse correlation between Tc and
petrologic type. We, thus, undertook a detailed study to
measure compositional properties of coexisting mineral
phases in several H4–H6 chondrites in order to constrain
their peak metamorphic temperatures and the high temperature cooling rates. In addition, we also model the available
data on the Fe–Mg ordering states of orthopyroxenes (Folco et al., 1996) to constrain the relatively low temperature
cooling rates of the different petrologic types. Finally we
show that a multistage cooling history model for the Hchondrite parent body (or bodies) is required to reconcile
the diverse set of petrological–kinetic constraints, as deduced in this study, and the available geochronological
data.
2. COMPOSITIONAL PROPERTIES OF MINERALS
AND THERMOMETRY
We studied in detail five H-chondrite samples, namely
Guarena (H6), Kernouvé (H6), Allegan (H5), Richardton
(H5), and Forest Vale (H4). These samples were also used
for thermochronological studies (Trieloff et al., 2003;
Kleine et al., 2008). The coexisting mineral pairs selected
for thermometric studies and compositional profile measurements are orthopyroxene–clinopyroxene (Opx–Cpx),
0.50
Guarena (H6)
Kernouvé
(H6)
X(Ca)
X(Ca)
0.40
Opx
Cpx
0.30
0.20
Opx
0.10
Cpx
0.00
0
5
10
0
5
10
15
20
25
30
35
15
20
25
30
35
1.00
0.90
Mg #
Mg #
0.95
0.85
0.80
0.75
0
5
10
15
20
25
Distance, µm
(a)
30
35
40
Distance, µm
(b)
Fig. 2. Representative compositional profiles of orthopyroxene (Opx)–clinopyroxene (Cpx) and orthopyroxene–spinel (Spnl) pairs
approximately normal to the respective interfaces. Mg#: Mg/(Mg + Fe), shown in enlarged scales. The points indicate spot analyses. (a)
Guarena (H6), Opx–Cpx; (b) Kernouvé (H6), Opx–Cpx; (c) Allegan (H5) Opx–Cpx and Opx–Spnl with Mg# and Fe# (1 Mg#) of Opx–
Spnl pair shown in an enlarged scale in lower right panel; (d) Forest Vale (H4) with Mg# for Opx and Spinel shown in enlarged scales.
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
209
(c)
Mg #
X(Ca)
Allegan
(H5)
Mg #
Opx
Opx
Cpx
Spnl
Distance, μ m
(d)
Distance, μm
1.00
Forest Vale
(H4)
Mg #
0.80
0.60
Opx
Spnl
0.40
0.20
0.00
Mg #
0
15
30
45
60
0.90
0.25
0.85
0.20
0.80
0.15
0
10
20
Distance, μm
30
10
20
30
40
50
60
Distance, µm
Fig. 2. (continued)
has much better counting statistics and resolution than SX50 and thus yields clearer BSE image. A BSE image of the
textural relation is shown in Fig. 3. Clinopyroxene grains
are present as thin laths within the groundmass and also
as rinds on orthopyroxene cores. The groundmass composition is variable and is roughly Ab50–85Kspar2–40An5–20.
It is also present as small inclusions within some clinopyroxene grains. (Upon reviewing this paper, Prof. Ozawa
commented that these textural relations suggest that Cpx
crystallized from interstitial melt that cooled at a high rate
with later morphological modification during cooling.)
Compositions obtained by averaging the data for line
scans in each coexisting pair of Opx–Cpx, Spnl–Opx and
Spnl–Ol, but excluding the data within 2 lm from the inter-
faces, which suffer from convolution effects, and sometimes
a few outlier data points, have been used to calculate equilibration temperatures of the respective mineral pairs. In a
few cases, additional temperatures were calculated using
data from distributed spot analyses of the mineral pairs.
The primary thermometric formulations used in this study
are:
(a) Anderson et al. (1993) for two-pyroxene (2-Px)
thermometry,
(b) Liermann and Ganguly (2003, 2007) for Opx–Spnl
Fe–Mg exchange thermometry (Eq. (5)), and
(c) Ballhaus et al. (1991) for Ol–Spnl Fe–Mg exchange
thermometry.
210
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
Fig. 3. Back scattered electron image of a portion of a thin section of Richardton showing clinopyroxene (Cpx) grains mantling
orthopyroxenes (Opx) and as small laths within a mesostasis (Meso) or groundmass of alkali rich plagioclase composition. The points
represent analytical points in a microprobe (red circles: Cpx, blue squares: Opx, green diamonds: mesostasis or groundmass). (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Each of these thermometric formulations has been based
on a large body of experimental data, and account for the
compositional effects arising from non-ideal thermodynamic mixing properties. The Ol–Spnl thermometric formulation of Ballhaus et al. (1991) incorporated the
experimental data of O’Neill and Wall (1987). The results
of these thermometric calculations are summarized in
Table 1 and illustrated in Fig. 4. Temperatures estimated
for individual mineral pairs according to a thermometric
method are listed below the Table 1. The temperature en-
Table 1
Summary of thermometric and age data for the meteorite samples studied in this work. Hf–W ages are relative to CAI formation age. The
parenthetical values represent 1 standard deviation (1r). All temperature calculations are based on average mineral compositions from line
scans (e.g. Fig. 2) and distributed spot analyses of coexisting minerals. Estimated temperatures for each mineral pair are listed below the table.
The average temperatures are listed in the table. The Ar–Ar ages could be older be 30 My because of a possible change of the decay constant
of K.
Meteorite
Type
T, °C
2-Px
Spnl–Opx
Spnl–Ol
Pb–Pb phosphate
Ar–Ar feldspars
Forest Vale
Forest Vale
Allegan
Richardton
Guarena
Kernouvé
H4
H4
H5
H5
H6
H6
757
757
817
877
848
848
746 (12)
746 (12)
643
602
632
653
709
709
614
555
565
607
4561
4561
4550
4551
4504
4522
4522
4522
4511
4495
4454
4469
(25)
(25)
(8)
(7)
(5)
(6)
Ages
(1)
(1)
(1)
(1)
(1)
(1)
(8)
(8)
(11)
(11)
(6)
(6)
Hf–W Dt(CAI)
5.6 (1.1)
9.4 (1.1)
2-Px: Forest Vale: 764(29), 738(50); Allegan: 808(17), 804(19), 819(34), 818(24), 827(12); Richardton: 925(36), 884)11), 941(36), 883(17),
893(21), 843(39), 869(26), 877(48), 847(27), 852(35), 863(42); Guarena: 853(56), 873(38), 853(18), 820(14), 847(6), 858(9); Kernouvé: 821(19),
861(10), 845(8). Opx–Spnl: Forest Vale: 728, 734, 773, 749; Allegan: 652, 637, 639; Richardton: 622, 58; Guarena: 627, 636; Kernouvé: 653.
Ol–Spnl: Forest Vale: 714, 703; Allegan: 601; Richardton: 555; Guarena: 565; Kernouvé: 607.
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
differences in the thermometric formulations and possibly
also quality of microprobe data. For example, Bunch and
Olsen (1974) determined the temperatures of Guarena
(H6) and Kernouvé (H6) as 780 and 920 °C, respectively.
But their analytical data yield 842 (±26) °C for Guarena
and 823 (±22) °C for Kernouvé when used in the program
of Anderson et al. (1993). The latter set of temperatures is
in good agreement with the results of this study (Table 1).
Some important results of thermometric calculations are
discussed below.
950
900
2-Px
850
T, C
800
750
700
Ol-Spnl
S&G
650
Opx-Spnl
600
Ol-Spnl
Ballhaus
550
500
3
4
5
6
211
7
Metamorphic Type
Fig. 4. Temperatures vs. petrologic types of H-chondrites according to orthopyroxene–clinopyroxene (red open squares), orthopyroxene–spinel (filled circles) and olivine–spinel thermometric
formulations (green triangles, open and filled). Vertical bars for
Opx–Cpx temperatures and Opx–Spnl temperature for H4 indicate
±2r error bars. S & G: Sack and Ghiorso (1991a, b). (For
interpretation of the references to color in this figure legend, the
reader is referred to the web version of this article.)
tries in the table represent the mean temperatures (weighted
mean for 2-Px thermometry) for a petrologic type according to a specific method.
The parenthetical numbers for 2-Px temperatures listed
below Table 1 represent 1r errors, as calculated by the program of Anderson et al. (1993). The weighted mean for 2Px temperature of each sample, along with the standard
deviation of the mean, are listed in Table 1. These have
been calculated according to the standard statistical methods (e.g. Bevington and Robinson, 2003). Errors of the
mean have not been estimated for the other thermometric
results, except for Opx–Spnl temperatures of Forest Vale,
since we determined temperatures for too limited number
of mineral pairs (63) for these samples. However, each of
these temperatures were determined from the average compositions of coexisting minerals obtained from line scans,
neglecting the data within 2 lm from the interface and
occasionally a few outliers. The standard deviation of the
mean for the Spnl–Opx temperatures for Forest Vale, for
which we estimated temperatures for four coexisting pairs
using average compositions from line scans, is calculated
assuming that the individual temperature estimates have
equal errors (Bevington and Robinson, 2003). This method
follows as a special case of that used to estimate error of the
weighted mean of 2-Px temperature. The true temperature
of a specific sample should be expected to lie, with 95% confidence, within the ±2r error envelope around the mean.
Earlier estimates of 2-Px temperatures of H-chondrites,
which have been summarized by Kessel et al. (2007), were
essentially restricted to H6 samples (there is no estimate
for H4 and one for H5), and based on formulations developed prior to the thorough experimental calibration of this
thermometer by Lindsley (1983). This is the first study of
H-chondrites utilizing the most thorough experimental calibration and thermodynamic formulation of 2-Px thermometer. As may be expected, there are usually considerable
differences between the results of earlier studies and this
study for the same samples, resulting primarily from
(a) The peak metamorphic temperatures determined for
the petrologic types 5 (Richardton and Allegan)
and 6 (Guarena and Kernouvé) by 2-Px thermometry
are higher than the peak temperature of type 4 (Forest Vale)), while, surprisingly, the reverse trend is
exhibited by Spnl–Opx/Ol Fe–Mg exchange thermometric results.
(b) The 2-Px and Spnl–Opx/Ol temperatures of H5
(Richardton and Allegan) are comparable to those
of H6 (Guarena and Kernouvé), with the 2-Px temperature of Allegan 30 °C lower and of Richardton
30 °C higher than that of the H6 samples. Thus,
there is no thermometric reason for the classification
of these H-chondrites into two petrologic types.
(c) The Spnl–Opx temperatures are somewhat higher
than those of Spnl–Ol temperatures for all samples,
with an average discrepancy of 50 °C (range 38–
67 °C). Similar discrepancy between the two thermometers was also noted by Liermann and Ganguly
(2003, 2007) for terrestrial ultramafic samples at temperatures above 900 °C.
As discussed above, Kessel et al. (2007) determined the
temperatures of a number of H-chondrites using the Ol–
Spnl thermometric formulation of Sack and Ghiorso
(1991a,b). These temperatures are much higher than the
Ol–Spnl and Opx–Spnl temperatures derived in this study
for the same petrologic types. Thus, we calculated the temperatures for three samples from the three petrologic types
(H4, H5, H6) using the Sack & Ghiorso formulation and
find that the temperatures are similar to those calculated
by Kessel et al. (2007). These temperatures are also illustrated in Fig. 4, which show the Ol–Spnl temperatures to
be still much lower than Opx–Cpx temperatures, except
for the petrologic type H4 (Forest Vale) for which all temperature estimates are similar. However, because of the
problem with the Ol–Spnl thermometric calibration, we
did not make any use of the temperatures derived from this
mineral pair in this study.
3. NUMERICAL SIMULATION OF THE
COMPOSITIONAL PROFILES IN COEXISTING
MINERAL PAIRS AND RETRIEVAL OF COOLING
RATES
3.1. Method and data
We have used the thermometric data summarized in
Table 1 and the compositional profiles of Opx–Cpx pairs
212
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
in H5 and H6 and of Opx–Spnl pair in H4 to constrain the
cooling rates of the H-chondrite samples. The choice of
Opx–Spnl pair for H4 is dictated by the fact that diffusion
in spinel is much faster than that in clinopyroxene so that a
cooling rate that preserves the peak temperature deduced
by Opx–Spnl thermometry must also do so for Opx–Cpx
pair with similar record of peak temperature. Additionally,
as discussed later, a satisfactory formulation of the temperature dependence of the Fe–Mg distribution coefficient between Opx and Cpx is still lacking for the type of Cpx
composition encountered in the H4 sample.
The observed homogeneity of the compositions across
the interface of the coexisting mineral pairs does not necessarily imply that the mineral compositions are completely
homogeneous. If the element fractionation between the
mineral pairs causes their Mg/(Mg + Fe) ratios, henceforth
referred to as Mg#, to recede from one another during
cooling, then the spatial averaging or convolution effect
stemming from the size of the excitation volume of the sample in microprobe analysis could damp the zoning profiles
very close to the interface. We present below numerical simulations for the development of compositional profiles in
Opx–Cpx pairs of Guarena (H6) and Allegan (H5), and
Spnl–Opx pair in Forest Vale (H4), with and without the
convolution effects. The convolution effect has been treated
according to the mathematical theory developed by Ganguly et al. (1988).
To determine the evolution of compositional profile during cooling, we solve the 1D diffusion equation for a binary
system in a Cartesian coordinate,
@C i
@
@C i
DðFe MgÞ
¼
ð1Þ
@X
@t
@X
where Ci is the concentration of a diffusing component (i)
and D(Fe–Mg) is the binary interdiffusion coefficient for
Fe and Mg. We assumed homogeneous initial concentrations of Fe and Mg in both minerals (a and b) in a coexisting pair, as determined by microprobe analyses of the
samples. The compositions of the two minerals at the interface were assumed to satisfy the distribution coefficient for
the Fe–Mg exchange reaction, which is given by
ðFe=MgÞa
K D ðFe MgÞ ¼
¼ f ðT Þ
ð2Þ
ðFe=MgÞb
An additional boundary condition is given by the
requirement that the flux of a component out of one phase
must equal that into the other phase:
a
b
@C i
@C i
¼ DðFe MgÞ
ð3Þ
DðFe MgÞ
@X
@X
There is no analytical solution of the diffusion equation
(Eq. (1)) for the above initial and boundary conditions. We,
therefore, developed a finite difference scheme according to
the widely used Crank–Nicolson implicit method (Crank,
1975) that is known to be unconditionally stable. The temperature dependence of KD(Fe–Mg) for Opx–Cpx pair is
derived in this study by combining the KD expressions for
Grt–Opx and Grt–Cpx pairs (Ganguly et al., 1996), and
is as follows.
2119
OpxðaÞCpxðbÞ
ðFe MgÞ ¼
ln K D
1:43
ð4Þ
T ðKÞ
This equation has been tested by comparing the temperatures, which results from its application to several samples,
with those derived from solvus thermometry for Opx–Cpx
(Lindsley, 1983; Anderson et al., 1993). Using the same
analytical data sets for Guarena (H6), Kernouvé (H6),
Richardton (H5) and Allegan (H5), the mean discrepancy
between the two sets of temperatures is 37 °C (range: 20–
50 °C). For Forest Vale (H4), the KD thermometry yields
absurdly high temperature that is 250 °C above the 2-Px
solvus temperature. The reason for this discrepancy for
the Forest Vale sample is not clear, but at least part of it
is most likely due to the relatively lower Ca content of
Cpx in this sample (X(CaSiO3) = 0.39) as compared to
the X(CaSiO3) = 0.46–0.47 for the others. The effect of lowering the Ca content of Cpx is to increase its Fe + Mg contents, with perhaps a somewhat greater increase of Fe than
Mg since Ca tends to substitute preferentially for Fe. It can
be shown that the net effect of lowering the Ca content is to
lower KD(Fe–Mg) in an Opx–Cpx pair and a corresponding
increase in the estimated value of temperature from Eq. (4).
For the Opx–Spnl pair, the temperature dependence of
KD has been taken from Liermann and Ganguly (2003),
and is as follows.
SpnðaÞOpxðbÞ
ðFe MgÞ
Ti
1174 1863 X Opx
þ 2309 Y Cr
Spnl þ 3037 X Spnl
Al
lnK D
¼
T ðKÞ
0:296 ð5Þ
where X Opx
Al stands for the mole fraction of Al in the octaheTi
dral site of othopyroxene, and Y Cr
Spnl and Y Spnl stand for the
mole fraction of Cr and Ti, respectively, in the octahedral
site of spinel. The compositional data for Opx do not suggest any significant octahedral Al, and thus the correction
for the effect of X Opx
Al has been neglected. In the numerical
simulations of Opx–Spnl pairs, we have treated the Y Cr
Spnl
and Y Ti
Spnl terms to be fixed by their initial values. In other
words, only Fe and Mg were allowed to exchange between
Opx and Spnl as the system cooled.
The diffusion coefficients for orthopyroxene, diopside
and spinel have been obtained from Ganguly and Tazzoli
(1994), Zhang et al. (2010) and Liermann and Ganguly
(2002), respectively. The appropriate diffusion data to use
for our calculations are those for Fe–Mg interdiffusion.
However, according to the results of Liermann and Ganguly (2002), the Fe and Mg self-diffusion in spinel are quite
similar, with D(Fe) being slightly greater than D(Mg).
Thus, instead of carrying out detailed calculations of
D(Fe–Mg) from the self-diffusion data, we approximated
it by D(Mg) since the value of an interdiffusion coefficient
is biased towards the diffusion coefficient of the dilute component (XMg(spnl) 0.2; see Fig. 2), as discussed, for example, by Ganguly (2002). We increased the D(Mg) of
Liermann and Ganguly (2002) by a factor of 10 to account
for the effect of Cr substitution, according to the results of
Suzuki et al. (2008). There are no (D(Fe–Mg) data for diopside, nor any D(Fe) data that can be combined with D(Mg)
to calculate D(Fe–Mg). Thus, we approximated D(Fe–Mg)
by D(Mg) for diopside. However, based on the difference
between D(Fe–Mg) and D(Mg) in other minerals (Ganguly
et al., 1998; Dohmen et al., 2007), this approximation of
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
corresponding to two different cooling rates, one showing
a very good match and the other showing a slight but measurable misfit to the measured profiles. In each case, the
(black) dashed line shows the simulated compositional profiles, whereas the solid (red) line shows the corresponding
convolved profile. The numerical simulations for the following cooling rates show very good agreement with the
measured profiles. Guarena (H6): 100 °C/ky; Allegan
(H5) 15 °C/ky; Forest Vale (H4): 50 °C/ky. The cooling
rate for Kernouvé (H6) is similar to that of Guarena. We
have not specifically modeled the flat concentration profile
D(Fe–Mg) by D(Mg) in diopside is not be expected to have
an effect on the calculation of cooling rates that could lead
to significant modification of our general conclusions.
3.2. Results
Fig. 5 shows the results of selected numerical simulations for the development of (quenched) compositional profiles in Opx–Cpx pairs in Guarena (H6) and Allegan (H5),
and in a Spnl–Opx pair in Forest Vale (4). For each pair,
we have illustrated the quenched convolved profiles
1.00
Mg #
0.96
(b) 1.00
Guarena (H6)
To = 850 oC
25 oC/ky &
100 oC/ky
0.92
0.88
Opx
Allegan (H5)
To = 820 oC
0.96
Mg #
(a)
213
0.5 oC/ky &
25 oC/ky
0.92
0.88
Opx
Cpx
Cpx
0.84
0.84
0.80
-25 -20 -15 -10
(c)
0.80
-5 0
5 10
Distance, μm
15
20
25
-25 -20 -15 -10
15
20
25
1.00
1 oC/ky &
50 oC/ky
0.80
Mg #
-5
0
5 10
Distance, μm
0.60
Forest Vale (H4)
To = 750 oC
Opx
0.40
Spnl
0.20
0.00
-30 -25 -20 -15 -10
-5
0
5
10
15
20
25
30
Distance, μm
Mg #
0.22
0.21
Spnl
0.20
-5
0
5
10
15
20
25
30
Distance, μm
Fig. 5. Numerical simulations of the development of compositional zoning in coexisting mineral pairs in three petrologic types for prescribed
cooling rates. In each panel, the dashed black line shows the calculated compositional profile for the slower cooling rate whereas the solid
black line shows the corresponding convolved profile; the solid red line shows the convolved profile for the faster cooling rate, matching the
analyzed data shown by open red circles. (a) Opx–Cpx pair in Guarena (H6) (b) Opx–Cpx pair in Allegan (H5) and (c) Opx–Spnl pair in
Forest Vale (H4), with the simulation in the spinel side shown in an enlarged scale. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
214
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
1.00
Mg #
0.96
Guarena (H6)
To = 850 oC
CR= 20 oC/My
0.92
0.88
0.84
0.80
-25
-20
-15
-10
-5
0
5
Distance, μ m
10
15
20
25
Fig. 6. Comparison of the measured compositional data (open
circles) of Opx–Cpx pair in Guarena (H6) with the quenched
compositional profile that developed in numerical simulation for
cooling at a rate of 20 °C/My, conforming to cooling in an onionshell parent body from a peak temperature of 850 °C. Dashed line:
simulated profile, solid line: convolved profile, open circle:
measured profile.
of an Opx–Cpx pair in Richardton, but from simple scaling
argument (t changes roughly as 1/D), the cooling rate for
Richardton should be 175 °C/ky because of its higher
peak temperature (877 °C) relative to Guarena (850 °C).
These cooling rates are 3–4 orders of magnitude faster than
those predicted for in situ cooling of the samples in an
onion shell parent body (Fig. 1).
The simulated concentration profile (Mg#) in Opx–Cpx
pair in Guarena for 20 °C/My cooling rate, conforming to
the in situ cooling in an onion shell parent body of 100 km
radius (Fig. 1), is compared with the measured data in
Fig. 6. The large difference between the simulated and measured concentration profiles strongly argues against the scenario of in situ cooling of Guarena in an onion shell parent
body.
justment of composition of the two minerals during cooling. For this purpose, we have recalculated Mg# values
for Opx–Spnl pair of Allegan (H5) corresponding to an initial temperature of 820 °C, and subjected it to a two stage
cooling process, as deduced above, that satisfy the Opx–
Cpx compositional profiles and the lower temperature
metallographic cooling data. The imposed cooling rates
are 25 °C/ky from 820 °C to 700 °C and 15 °C/My at lower
temperature. The result of the simulation is shown in Fig. 7.
The final spinel composition is found to match the observed
composition, but there is a slight but measurable mismatch
between the observed and simulated compositions of orthopyroxene. The complete resolution of the problem of
resetting of Opx–Spnl thermometer has to await further
analysis, but it is not critical to the main objectives of this
paper.
4. ADDITIONAL CONSTRAINTS ON COOLING
RATES
4.1. Metallographic data
Krot et al. (2012) have recently determined the cooling
rates from metallographic data for a number of H3–H6
chondrites that include the H-chondrites investigated in this
work. The inferred cooling rates, which are strictly applicable within a limited temperature domain around 550 °C, are
as follows. Forest Vale (H4): 104 °C/My; Allegan (H5):
15 °C/My; Guarena (H6): 15 °C/My; Kernouvé (H6):
10 °C/My. The metallographic cooling rate for Forest Vale
is found to be in very good agreement with the cooling rate
(5 104 °C/My) calculated above from modeling flat
concentration profile of Mg in Opx–Spnl pair. The apparent discrepancy for the H5 and H6 samples implies that
the cooling rates of these samples drastically slowed down
by major changes of their physical environments during
3.3. The Problem of Resetting of Opx-Snl Temperatures
1.00
We have explored if the observed resetting of Opx–Spnl
Fe–Mg exchange thermometer could be achieved by readMg #
0.96
1.0
Guarena (H6)
To = 850 oC
0.92
0.88
0.8
Mg #
0.84
0.6
0.4
Opx
Spnl
0.2
0.0
-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30
Distance, μm
Fig. 7. Simulation of the resetting of Opx–Spnl compositions in
Allegan (H5) through Fe–Mg exchange during a process of twostage cooling as deduced in this work. The cooling rate is 25 °C/ky
between 820 and 700 °C and 15 °C/My at lower temperature. The
dashed horizontal lines show reconstructed initial compositions
satisfying the KD value at 820 °C. Open circles: measured data.
0.80
-25 -20 -15 -10
-5
0
5
Distance, μ m
10
15
20
25
Fig. 8. Numerical simulation of the compositional profile in Opx–
Cpx pair, conforming to metallographic cooling rate of 15 °C/My
at low temperature and 100 °C/ky cooling rate at high temperature
(Fig. 5a). The transition to slow cooling is set at 700 °C (top dashed
and solid curves) and 650 °C. The convolved profile for the latter is
indistinguishable from that for a uniform cooling rate of 100 °C/
ky, which is shown by a solid red line. As in other figures, a dashed
curve indicates a simulated profile whereas a solid curve indicates a
convolved profile. (For interpretation of the references to color in
this figure legend, the reader is referred to the web version of this
article.)
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
cooling. The likely scenario for such changes has been discussed later. Here we explore if the simulated compositional
profiles at high temperature deduced in this study to conform to the observed profiles could be preserved by a second stage of slow cooling beginning at some temperature
above 550 °C. The threshold temperature above which the
compositional profile gets disturbed by the second stage
of slow cooling determines the upper limit of temperature
for the domain of validity of the metallographic cooling
rate.
Fig. 8 shows two-stage cooling profiles for Mg# in Opx–
Cpx pair in Guarena (H6), starting with a cooling rate of
100 °C/ky at the peak temperature of 850 °C, as deduced
above (Fig. 5a), and changing to 15 °C/My at 650 °C or
750 °C. The convolution of the simulated concentration
profile matches the measured profile if the transition to
slow cooling takes place at 650 °C, whereas it deviates
slightly, but measurably, from the observed profile near
the interface if the transition temperature is set to 750 °C.
We, thus, conclude that the transition to slow cooling for
Guarena (H6) and Allegan (H5), which have been deduced
from metallographic studies, had taken place at a temperature no higher than 700 °C.
4.2. Fe–Mg ordering data in orthopyroxene
In orthopyroxenes, Fe2+ (henceforth referred to as Fe)
and Mg fractionate between two nonequivalent crystallographic sites, M2 and M1, with a preference for the former
by Fe and for the latter by Mg (Ghose, 1962). The fractionation is temperature sensitive, and can be described by an
intracrystalline exchange reaction
FeðM1Þ þ MgðM2Þ $ FeðM2Þ þ MgðM1Þ;
ðaÞ
which is driven progressively to the right with decreasing
temperature. Building upon the chemical rate theory of order–disorder by Mueller (1967), Ganguly (1982) developed
a method of retrieving cooling rates of host rocks from the
quenched Fe–Mg ordering states of orthopyroxenes. The
method has subsequently been applied to a number of terrestrial and meteorite samples (e.g. Ganguly et al., 1994;
Molin et al., 1994; Ganguly and Domeneghetti, 1996) and
also verified against independent geochronological constraints (Stimpfl et al., 2005).
Folco et al. (1996) determined the quenched Fe–Mg
ordering states of orthopyroxenes of a number of unshocked equilibrated H-chondrites by single crystal structure
refinement. They calculated the final equilibration or closure temperatures of ordering (Tc(ord)) of orthopyroxenes
from metamorphic types 4, 5 and 6, but did not find any
correlation between this parameter and the metamorphic
type, which is in contrast to the inverse correlation that is
expected for an onion-shell parent body model (Fig. 1).
Folco et al. (1996) thus concluded that the H-chondrite
samples investigated by them cooled in similar environments, regardless of the degree of metamorphism.
Using the most thorough calibration of the intracrystalline distribution coefficient, which is defined according to
(a) as kD = (Fe/Mg)M2/(Fe/Mg)M1), as a function of temperature (Stimpfl et al., 1999), we have recalculated Tc(ord)
215
Fig. 9. Closure temperatures of Fe–Mg ordering in orthopyroxenes from different petrologic types of H-chondrites.
of the orthopyroxenes from the metamorphic types 4–6. As
in the study of Folco et al. (1996), our results, which are
illustrated in Fig. 9, do not show any correlation between
Tc(ord) vs. metamorphic grade. However, the calculated
Tc(ord) values in our calculation are systematically greater
than those in Folco et al. (1996), reflecting the difference between the thermometric calibrations. Noting that a cooling
rate reflected by a temperature sensitive property, such as
cation ordering state of orthopyroxene, is strictly valid at
temperatures around the closure temperature of that property, we conclude from Fig. 9 that the metamorphic types 4,
5 and 6 have similar cooling rates at temperatures around
500 °C.
Using the kinetic and thermodynamic parameters governing the intracrystalline Fe–Mg exchange in orthopyroxene (Stimpfl et al., 1999, 2005) and the theoretical
formulation and numerical method developed earlier
(Mueller, 1967; Ganguly, 1982), we have calculated the
change of ordering state vs. T during monotonic cooling
for selected orthopyroxene grains from H-chondrites of
metamorphic types 4 and 6. The cooling was assumed to
conform to an asymptotic form, 1/T = 1/To + gt where g
is a cooling time constant with dimension of K1 t1. We
did not change the form of the cooling rate to the linear
form that is used in the modeling of compositional zoning,
since our computer code for this problem is set up according to the asymptotic form of cooling rate. However, within
the limited temperature domain around the Tc(ordering)
over which the retrieved T–t relation is expected to be valid,
the deviation from linearity is not significant for the general
purpose of this modeling.
The chemical and ordering data for the orthopyroxene
grains are taken from Folco et al. (1996). The chosen data
show the largest variation of ordering states within a given
metamorphic type. We simulated the evolution of M2
site occupancy of Fe vs. T such that the quenched site
occupancy value in the simulations match the observed
data within their 1r error limits, and the cooling rates at
Tc(ord) are as close as possible for samples from the same
metamorphic type. The results are illustrated in Fig. 10.
These cooling rates, again, are orders of magnitude faster
than those depicted in an “onion shell” parent body model
(Fig. 1).
The cooling rates determined from Fe–Mg ordering data
in orthopyroxenes may be compared with those determined
216
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
650
A314-8 (H6)
CR: ~ 15 C/Ky
at Tc (~ 475 C);
η = 2.7E-8 K-1y-1
600
T, C
550
500
600
550
EST7 (H6)
CR: ~ 17 C/Ky
at Tc (~ 475 C);
η = 3.0E-8 K-1y-1
500
450
450
400
400
350
350
300
0.324 0.328 0.332 0.336 0.340 0.344
300
0.324 0.328 0.332 0.336 0.340 0.344
650
LV11 (H4)
CR: ~ 54 C/Ky
at Tc (~ 543 C);
-1 -1
η = 9E-8 K y
600
550
T, C
650
500
FM76-15 (H4)
CR: ~ 18 C/Ky
at Tc (~ 543 C;
η = 3E-8 K -1y-1
450
400
350
300
0.300
0.304
0.308
0.312
0.316
0.320
X(Fe)M2
0.308 0.312 0.316 0.320 0.324 0.328 0.332
X(Fe)M2
Fig. 10. Simulation of the change of cation ordering states of selected H6 and H4 chondrites for prescribed monotonic T–t relations that
produce quenched ordering states matching the observed data (filled squares with error bars). The latter are fitted within 1r errors such that
there is least disparity between the cooling rates retrieved from samples of the same metamorphic type at their respective closure temperatures.
by metallographic method (Krot et al., 2012) since both
methods are applicable to limited temperature range
around 550 °C. We find that while the cooling rates for
the H4 samples are similar to those determined by the
metallographic method, those for the H6 samples are three
orders of magnitude larger than the metallographic rates.
The reason for this discrepancy is not clear, but the metallographic cooling rates were determined for H6 samples
that are different from those studied by Folco et al.
(1996). Thus, one cannot rule out the possibility that even
at temperatures around 500 °C, some H6 samples cooled
at a rate much faster than those studied by the metallographic method. A comparison between the results obtained by the two methods for the same sample would be
instructive.
5. THERMOMETRIC AND COOLING RATE
CONSTRAINTS VS. GEOCHRONOLOGICAL DATA
AND IMPLICATIONS
5.1. Hf–W ages vs. peak temperatures of H5 and H6
chondrites
The Hf–W age of Richardton (H5) is older than that of
Kernouvé (H6) by 4 ± 1.4 Ma, but the peak metamorphic
temperatures of these samples, as calculated by 2-Px thermometer, are similar (Table 1); if there is any real difference, then the T(peak) of Richardton, calculated to be
875 °C, is probably higher than that of Kernouvé
(850 °C). Kleine et al. (2008) argued that the Hf–W decay
system records the peak metamorphic ages of H5/6-chon-
drites. In that case the above data for T(peak) and Hf–W
ages pose an obvious paradox, if the two samples were derived from the same parent body, in that the calculated
T(peak) of Richardton requires that it was buried at about
the same depth as or somewhat deeper than Kernouvé,
whereas its older peak metamorphic age requires that it
was derived from a shallower level than Kernouvé
(Fig. 1). If 26Al decay was essentially the sole reason for
heating of parent asteroids, then the resolution of this paradox requires that either the two samples were derived from
different parent bodies, with that of Richardton probably
accreting somewhat earlier than the parent body of Kernouvé, or that there was inhomogeneous distribution of
26
Al in the single parent body in which Richardton was buried in a region that was shallower than the source region of
Kernouvé but had higher 26Al concentration. The second
model retains the commonly held notion (e.g. Wasson,
1985; Trieloff et al., 2003) that because of their chemical
similarities, the samples belonging to the same chemical
group (H, L and LL) were derived from the same parent
body, but argues against the common practice of calculating the thermal evolution of the parent body assuming
homogeneous distribution of the heat producing isotopes.
5.2. Comparison of the thermochronological data with the
inferred cooling rates of H-chondrites and a multistage
cooling model
We now compare the thermometric data and cooling rate
constraints derived above with the available thermochronological data to develop a comprehensive understanding of
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
217
900
800
H6
700
H5
T, C
600
500
+ Phosphate Pb-Pb Ages
H4
400
O, Δ: H5
300
200
100
4580
Feldspar Ar-Ar
Ages
: H4
X,
4530
+: H6
4480
4430
Time b.p (Myr)
Fig. 11. Integrated cooling paths of H4 (Forest Vale), H5 (Allegan and Richardton) and H6 (Guarena and Kernouvé) samples, as constrained
by the high temperature cooling rates, deduced in this study, metallographic cooling rates and geochronological data, which are summarized
in Table 1. The Pb–Pb ages of the two H5 samples, Allegan and Richardton, are indistinguishable in the plot. The closure temperatures of the
Pb–Pb ages have been calculated in this study using the inferred cooling rates and observed average grain size (r = 20 lm). Smaller effective
diffusion distance leads to lower Tc-s (25 °C lower for r = 10 lm). The spread in the Ar–Ar ages of each sample stems from the uncertainty
of the decay constant of K.
the cooling history of the H-chondrites through a large
span of temperature and then explore the implications in
terms of parent body processes. Fig. 11 shows a comparison
of the T–t paths constrained by the thermometric data and
diffusion modeling with the Pb–Pb model ages of phosphates (Göpel et al., 1994) and Ar–Ar ages of feldspars
(Trieloff et al., 2003) vs. the respective closure temperatures
(Tc) for the H4, 5, and 6 samples. There is a large spread of
the Ar–Ar age of each sample stemming from the uncertainty in the decay constant of K. Trieloff et al. (2003) argued that the Ar–Ar ages of the feldspars could be older
by 30 My than the reported ages. Göpel et al. (1994) and
Trieloff et al. (2003) assumed conventional closure temperatures of 470 and 277 °C for Pb–Pb and Ar–Ar ages,
respectively, regardless of their T–t paths. However, unless
the cooling rate exceeds a critical limit, Tc has significant
dependence on cooling rate. The commonly assumed or
conventional single-Tc value of a decay system reflects, at
best, a closure temperature that is likely to hold for certain
ranges of the values of the governing factors (To, grain size
and cooling rate) that are usually encountered in natural
problems. We recalculated the Tc-s for the Pb–Pb ages of
phosphates using the observed grain size and the cooling
rate constraints. These calculations are discussed below.
The peak metamorphic ages of the H5 and H6 samples,
as shown in Fig. 11, have been constrained by the Hf–W
ages relative to CAI-s, as determined by Kleine et al.
(2008), and the CAI formation of age (4567.2 ± 1(2r)) given by Amelin et al. (2010). From consideration of possible
diffusion kinetics of W in the primary host minerals, it has
been argued by Kleine et al. (2008) that the Hf–W ages of
H5 and H6 samples reflect their peak metamorphic ages.
However, according to them, the Hf–W age of the H4 sample, Ste Marguerite, does not reflect the peak metamorphic
age, but instead reflects the timing of an earlier high temperature event, i.e. chondrule formation. Thus, for H4
(Forest Vale), we have used the phosphate Pb–Pb age since,
as shown below, no significant resetting of the Pb–Pb age
could have been possible during the very rapid cooling of
this sample, as determined in this study and by metallographic method (Krot et al., 2012). However, for clarity
of presentation, we have raised the Pb–Pb age of Forest
Vale by 3 My, which is within the 2r error limit (i.e.
4 My) of the age data. For H5 and H6, we have used the
Hf–W ages determined for Richardton and Kernouvé,
respectively, instead of the average ages for these metamorphic types, as we have also calculated the T–t paths of these
samples.
Using the theoretical formulations of Dodson (1973)
and Ganguly and Tirone (1991, 2001), Pb diffusion data
in apatite by Cherniak et al. (1991), the observed average
grain radius of 20 lm (Göpel et al., 1994), and the inferred cooling rates, we have calculated the Tc-s for Pb diffusion in phosphates in the H-chondrite samples. For
Forest Vale (H4), the Tc is found to be essentially the same
as the peak temperature (745 °C vs. To = 750 °C), whereas
for H5 and H6, the Tc is 455 °C (Fig. 11). In these calculations, we have used a spherical geometry that maximizes
diffusive flux out of a mineral grain, and as a result the
Tc values might have been somewhat underestimated. The
calculated Tc for H4 is 270 °C higher than the conventional
value whereas for H5/6, it is similar to the latter.
As evident from Fig. 11, the T–t path of Forest Vale
(H4) based on a constant cooling rate of 50 °C/ky satisfies
all data, viz. compositional profiles in Cpx–Opx pairs,
metallographic cooling rate at 550 °C, Pb–Pb age data for
phosphates and Ar–Ar age data for feldspars. For H5,
the T–t path constructed by imposing the metallographic
218
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
cooling rate (15 °C/My) from 700 °C satisfies the age vs. Tc
data for both Pb–Pb and Ar–Ar systems. However, for the
H6 samples, the metallographic cooling rate of 15 °C/My
commencing at 700 °C does not satisfy the Pb–Pb age data
for phosphates and Ar–Ar age data for feldspars. To satisfy
these data, we need at least one more stage of slower cooling commencing at some temperature below 550 °C. In
Fig. 11, we illustrate a T–t path using a cooling rate of
3 °C/My that satisfies, within errors, all low temperature
age vs. Tc data. It is also possible that the effective diffusion
distance (EDC) of Pb within the phosphates is smaller than
their grain sizes. In that case the Tc for the Pb–Pb ages
would be lower than those calculated above. For example,
if the EDC is half of the observed grain size (10 lm), then
the Tc-s for H5 and H6 samples are reduced by 25 °C.
This permits a better match between the age vs. Tc data
and the cooling T–t path.
6. A FRAGMENTATION-REASSEMBLY MODEL OF
THE H-CHONDRITE PARENT BODY
The multistage cooling model for the H-chondrites illustrated in Fig. 11 cannot be explained by simple monotonic
cooling at different depths in an onion-shell parent asteroid,
with the higher grade rocks buried at progressively greater
depths (Fig. 1), but instead requires a complex history of
fragmentation and reassembly of the parent body. A possible model of such parent body process is presented below.
In accordance with the data on chemical similarities of
the H-chondrites, as discussed above, we assume that the
samples were derived from a single parent body. However,
the complexity of the model is not reduced by invoking different parent bodies.
(a) The initial very rapid cooling rates of H4–H6 samples
could be achieved by the excavation of the parent
body by an impact, thereby leading to the exposure
of the samples to near surface conditions. The much
faster cooling of the H4 (Forest Vale) sample compared to the H5/6 samples might have been due to
its ejection to the surface or the penetration of the
excavation depth to the H4 layer in an onion-shell
parent body.
(b) The slow cooling of 15 °C/My commencing at
700 °C for the H5/6 samples (Fig. 11) could have
been due to accretion/accumulation of material on
the excavated rocks at this stage or reassembly of
the material into a new parent body following their
ejection after one or more additional impacts. In
the reassembled parent body, the H6 samples (Guarena and Kernouvé) might have been buried deeper,
thus permitting slower cooling and greater resetting
of their Pb–Pb phosphate age relative to the H5
samples.
(c) The final stage of even slower cooling of a few
degrees per My for the H6 samples (Fig. 11) might
imply another episode of accretion of material on
the H6 samples or burial under a thick regolith blanket that has low thermal conductivity with the regolith material resulting from an impact.
Nakamura et al. (2011) have recently reported the mineralogy and mineral chemistry of the dust particles scooped
from the Asteroid Itokawa. They found the mineralogical
properties to be indicative of high temperature metamorphism at 800 °C and classified the dust particles as LL5
and LL6. Since such high temperature requires deep burial
in an Asteroidal parent body heated by 26Al decay, Nakamura et al. (2011) suggested that the surface material of Itokawa was originally buried deep in a much larger asteroid,
which was catastrophically disaggregated by one or more
impact events, and that some of the impact pieces were then
re-accreted into the greatly diminished rubble-pile asteroid
that is now Itokawa. This scenario and the discovery of
metamorphic types 5 and 6 on the surface of an asteroid
give credence to the fragmentation-reassembly model of
the parent body that we have presented above. Additionally, there is no obvious reason as to why the process of
re-accretion should be restricted to the materials ejected
from a single parent body; it is quite possible that there
was mixing of materials derived from different parent
bodies to form new asteroids.
The T–t path presented in Fig. 11 is qualitatively similar
to that developed by Ganguly et al. (1994) for the parent
body of mesosiderites, which is characterized by very rapid
cooling of several degrees per ky from 1150 °C, followed
by very slow cooling at 1 °C/My at 725 °C. This similarity may suggestive of some common scenario in the fragmentation and re-accretion/regolith blanketing in the
early history of asteroids.
7. SUMMARY AND CONCLUSIONS
The important conclusions that have emerged from the
analysis of mineralogical properties and their comparison
with metallographic cooling rates and geochronological
constraints may be summarized as follows.
(a) The H4 sample, Forest Vale, has distinctly lower
peak temperature than the H5 (Richardton and Allegen) and H6 (Guarena and Kernouvé) samples,
whereas there is no significant difference between
the peak temperatures of the last two groups
(Fig. 4). (This study should also prompt careful
determination of the peak metamorphic temperatures
of other H5 and H6 samples.)
(b) While the 2-Px and Spnl–Opx /Ol thermometric temperatures are mutually compatible for the H4 sample,
they diverge in opposite directions for the H5 and H6
samples (Fig. 4). The discrepancy between the two
types of thermometric results for the H5/6 samples
is due to the resetting of spinel compositions during
slow cooling below 700 °C, but a completely satisfactory model of the compositional readjustment of the
thermometric pairs is still lacking.
(c) For the H4 sample all cooling rate constraints
derived from modeling compositional zoning and
metallographic data are mutually compatible and
the consequent T–t path also agrees with all geochronological data (Pb–Pb and Ar–Ar ages vs. Tc-s). The
very rapid cooling of 50 °C/ky inferred for this
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
sample suggests cooling under near surface environment, effectively through the entire temperature
range.
(d) The very rapid cooling rates of 25–100 °C/ky of the
H5/6 samples down to 700 °C that are constrained
by modeling compositional profiles of coexisting
Opx–Cpx pairs are incompatible with the commonly
held notion of in situ slow cooling of the different petrologic types at different depths in an onion-shell parent body.
(e) Assuming that the decay of 26Al was the principal
mechanism of heating of an asteroid, the relative
peak metamorphic temperatures and Hf–W ages of
Richardton (H5) and Kernouvé (H6) seem to imply
that either the two samples were derived from different parent bodies, with that of Richardton probably
accreting somewhat earlier, or that there was inhomogeneous distribution of 26Al within a single parent
body of the two samples in which Richardton was
buried at a shallower depth than Kernouvé (H6),
but in a region with higher 26Al concentration.
(f) The T–t paths constrained by thermometric and cooling rate constraints of the H5 (Allegan and Richardton) and H6 (Guarena and Kernouvé) chondrites, as
determined in this study and from metallographic
data (Krot et al., 2012), could be reconciled with
the available thermochronological data, except for
the whole rock Pb–Pb age data, through a process
of multistage cooling that could have been due to
the following processes:
(i)
Impact induced fragmentation/deep excavation of the parent body shortly after the attainment of the peak temperatures, followed by
(ii) accumulation or accretion of material on the
excavated rocks when the latter had cooled to
700 °C, or impact-ejection at this stage and
reassembly into a separate parent body leading
to slow cooling, and
(iii) subsequent re-accretion of asteroidal material
on, or impact induced regolith blanketing of,
the H6 samples.
Our model is not incompatible with onion-shell parent
body structure at the initial stage, but it represents a major
paradigm shift in the interpretation of the low temperature
thermochronological data in terms of in situ cooling in an
onion-shell parent body. The general form of the cooling
paths for H5 and H6 samples, characterized by very rapid
cooling at high temperature (25–100 °C/ky) followed by
much slower cooling commencing at 700 °C (15 °C/
My) is similar to that deduced for mesosiderites, which
are stony-iron meteorites, by Ganguly et al. (1994).
ACKNOWLEDGMENTS
This research was initiated while the senior author was a visiting scientist in the R}
uhr University, Bochum, Germany, with support from Alexander von Humboldt Foundation, which is
gratefully acknowledged. Continuation of the work at the University of Arizona was supported by NASA Grants NNX10AI79G
219
and NNX07AJ74G. Thanks are due to H.-J. Bernhardt of the
R}
uhr University for his help with some of the microprobe analyses.
The meteorite samples used in this study were kindly provided by
Dr. Jutta Zipfel, Senckenberg Museum, Frankfurt, Germany,
and the Smithsonian Institution, Washington, USA. We are grateful to Drs. Thorsten Kleine, Bruce Watson and Kazuhito Ozawa
for very thoughtful and constructive reviews and Dr. Hiroko Nagahara for her editorial handling and comments that have lead to major improvements of both the scientific content and the
presentation of the manuscript.
REFERENCES
Amelin Y., Kaltenbach A., Lizuka T., Stirling C. H., Ireland T. R.,
Pataev M. and Jacobsen S. B. (2010) U–Pb chronology of the
Solar System’s oldest solids with variable 238U/235U. Earth
Planet. Sci. Lett. 300, 343–350.
Anderson D. J., Lindsley D. H. and Davidson P. M. (1993)
QUILF: A Pascal program to assess equilibria among Fe–Mg–
Mn–Tic oxides, pyroxenes, olivines and quartz. Comput.
Geosci. 19, 1333–1350.
Ballhaus C., Berry R. F. and Green D. H. (1991) High temperature
experimental calibration of the olivine–orthopyroxene–spinel
oxygen barometer: Implications for the oxidation state of the
upper mantle. Contrib. Mineral Petrol. 107, 27–40.
Bevington P. R. and Robinson O. K. (2003) Data Reduction and
Error Analysis for the Physical Sciences. Mc-Graw Hill, 307p.
Bunch T. E. and Olsen E. (1974) Restudy of pyroxene–pyroxene
equilibration temperatures for ordinary chondritic meteorites.
Contrib. Mineral. Petrol. 43, 83–90.
Cherniak D. J., Lanford W. and Ryerson F. J. (1991) Lead
diffusion in apatite and zircon using ion implantation and
Rutherford backscattering techniques. Geochim. Cosmochim.
Acta 55, 1663–1673.
Crank J. (1975) The Mathematics of Diffusion, second ed. Oxford.
Dodson M. H. (1973) Closure temperature in cooling geochronological and petrological systems. Contrib. Mineral. Petrol. 40,
259–264.
Dohmen R., Becker H. W. and Chakraborty S. (2007) Fe–Mg
diffusion in olivine I: Experimental determination between 700
and 1200 degrees C as a function of composition, crystal
orientation and oxygen fugacity. Phys. Chem. Mineral. 34, 389–
407.
Folco L., Melini M. and Pillinger C. T. (1996) Unshocked
equilibrated H-chondrites: A common low-temperature record
from orthopyroxene iron–magnesium ordering. Meteor. Planet.
Sci. 31, 388–393.
Ganguly J. (2002) Diffusion kinetics in minerals: Principles and
applications to tectono-metamorphic processes. In Energy
Modeling in Minerals, EMU Notes in Mineralogy, vol. 4 (ed.
C. M. Gramaccioli), Eötvös University Press, Budapest, pp.
271–309.
Ganguly J. and Tirone M. (2001) Relationship between cooling
rate and cooling age of a mineral: Theory and applications to
meteorites. Meteor. Planet. Sci. 36, 167–175.
Ganguly J. and Tirone M. (1999) Diffusion closure temperature
and age of a mineral with arbitrary extent of diffusion. Earth
Planet. Sci. Lett. 170, 131–140.
Ganguly J., Cheng W. and Chakraborty S. (1998) Cation diffusion
in aluminosilicate garnets: Experimental determination in
pyrope–almandine diffusion couples. Contrib. Mineral. Petrol.
131, 171–180.
Ganguly J., Cheng W. and Tirone M. (1996) Thermodynamics of
aluminosilicate garnet solid solution: New experimental data,
220
J. Ganguly et al. / Geochimica et Cosmochimica Acta 105 (2013) 206–220
an optimized model and thermometric applications. Contrib.
Mineral. Petrol. 26, 137–151.
Ganguly J., Yang H. and Ghose S. (1994) Thermal history of
mesosiderites: Quantitative constraints from compositional
zoning and Fe–Mg ordering in orthopyroxenes. Geochim.
Cosmochim. Acta 58, 2711–2723.
Ganguly J. and Domeneghetti M. C. (1996) Cation ordering of
orthopyroxenes from the Skaergaard intrusion: Implications
for the subsolidus cooling rates and permeabilities. Contrib.
Mineral. Petrol. 122, 359–367.
Ganguly J. and Tazzoli V. (1994) Fe2+–Mg interdiffusion in
orthopyroxene: Retrieval from the data on intracrystalline
exchange reaction. Am. Mineral. 79, 930–937.
Ganguly J., Bhattacharya R. N. and Chakraborty S. (1988)
Convolution effect in the determination of compositional
profiles and diffusion coefficients by microprobe step scans.
Amer. Mineral. 73, 901–909.
Ganguly J. (1982) Mg-Fe order–disorder in ferromagnesian
silicates. II. Thermodynamics, kinetics and geological applications. In Advances in Physical Geochemistry, vol. 2 (ed. S. K.
Saxena), pp. 58–99. Advances in Physical Geochemistry.
Springer-Verlag, Berlin, Heidelberg, New York.
Ghose S. (1962) The nature of Fe2+–Mg2+ distribution in some
ferromagnesian silicate minerals. Am. Mineral. 47, 388–394.
Göpel C., Manhès G. and Allègre C. J. (1994) U–Pb systematics of
phosphates from equilibrated ordinary chondrites. Earth
Planet. Sci. Lett. 121, 153–171.
Kessel R., Beckett J. and Stolper E. M. (2007) The thermal history
of equilibrated ordinary chondrites and the relationship
between textural maturity and temperature. Geochim. Cosmochim. Acta 71, 1855–1881.
Kleine K., Touboul M., Van Orman J. A., Bourdon B., Maden C.,
Mezger K. and Halliday A. N. (2008) Hf–W thermochronometry: Closure temperature and constraints on the accretion and
cooling history of the H chondrite parent body. Earth Planet.
Sci. Lett. 270, 106–118.
Krot T. A., Goldstein J. J., Scott E. R. D., Wakita S. (2012)
Thermal histories of H3–H6 chondrites and their parent
asteroid from metallographic cooling rates and cloudy taenite
dimensions. In 75th Annual Meteoritical Society Meeting.
#5372 (abstr.).
Liermann H.-P. and Ganguly J. (2007) Erratum: Fe2+–Mg
fractionation between orthopyroxene and spinel: Experimental
calibration in the system FeO–MgO–Al2O3–Cr2O3–SiO2, and
applications. Contrib. Mineral. Petrol. 154, 491.
Liermann H.-P. and Ganguly J. (2003) Fe2+–Mg fractionation
between orthopyroxene and spinel: Experimental calibration in
the system FeO–MgO–Al2O3–Cr2O3–SiO2, and applications.
Contrib. Mineral. Petrol. 145, 217–227.
Liermann H.-P. and Ganguly J. (2002) Diffusion kinetics of Fe2+
and Mg in aluminous spinel: Experimental determination and
applications. Geochim. Cosmochim. Acta 66, 2003–2013.
Lindsley D. H. (1983) Pyroxene thermometry. Am. Mineral. 68,
477–493.
Lipschutz M. E., Gaffey M. E. and Pellas P. (1989) Meteoritic
parent bodies: Nature, number, size and relation to present-day
asteroids. In Asteroids (eds. R. P. Brinzel, T. Gehrels and M. S.
Mathews). Univ. Arizona Press, Tucson, Arizona, pp. 740–778.
Molin G. M., Tribaudino M. and Brizi E. (1994) Zaoyang
chondrite cooling history from Fe2+–Mg intracrystalline ordering in pyroxenes. Mineral. Mag. 58, 143–150.
Mueller R. F. (1967) Model for order–disorder kinetics incertain
quasibinary crystals of continuously variable composition. J.
Phys. Chem. Solids 28, 2239–2243.
Nakamura T., Noguchi T., Tanaka M., Zolensky M. E., Tsuchiyama M. A., Nakato A., Ogami T., Ishida H., Uesugi M.,
Fujimura A., Okazaki R., Sandford S. A., Ishibashi Y., Abe
M., Ueno M., Mukai T., Yoshikawa M. and Kawaguchi J.
(2011) Itokawa dust particles: A direct link between S-type aste
ordinary chondrites. Science 333, 1113–1116.
O’Neill H. St. C. and Wall V. J. (1987) The olivine–orthopyroxene–
spinel oxygen geobarometer, the nickel partition curve, and the
oxygen fugacity of the Earth’s upper mantle. J. Petrol. 28,
1169–1191.
Sack R. O. and Ghiorso M. S. (1991a) An internally consistent
model for the thermodynamic properties of Fe–Mg–titanomagnetite–aluminate spinels. Contrib. Mineral. Petrol. 106, 474–
505.
Sack R. O. and Ghiorso M. S. (1991b) Chromium spinels as
petrogenic indicators: Thermodynamics and petrological applications. Am. Mineral. 76, 827–847.
Stimpfl M., Ganguly J. and Molin G. (2005) Kinetics of Fe2+–Mg
order–disorder in orthopyroxene: Experimental studies and
applications to cooling rates of rocks. Contrib. Mineral. Petrol.
150, 319–334.
Stimpfl M., Ganguly J. and Molin G. (1999) Fe2+–Mg order–
disorder in orthopyroxene: Equilibrium fractionation between
the octahedral sites and thermodynamic analysis. Contrib.
Mineral. Petrol. 136, 297–309.
Suzuki et al. (2008) Cr and Al diffusion in chromite spinel:
Experimental determination and its implication for diffusion
creep. Phys. Chem. Miner. 35, 433–445.
Taylor G. J., Maggiore P., Scott E. R. D., Rubin A. E. and Keil K.
(1987) Original structures and fragmentation and reassembly of
asteroids: Evidence from meteorites. Icarus 69, 1–13.
Trieloff M., Jesserberger E. K., Herrwerth I., Hopp J., Fiénl C.,
Ghélls M., Bourot-Denise M. and Pellas P. (2003) Structure
and thermal history of the H-chondrite parent asteroid revealed
by thermochronometry. Nature 422, 502–506.
Wasson J. T. (1985) Meteorites: Their Record of Early SolarSystem History. Freeman & Co., New York.
Zhang X.-Y., Ganguly J. and Ito M. (2010) Ca–Mg diffusion in
diopside: Tracer and chemical inter-diffusion coefficients. Contrib. Mineral. Petrol. 159, 175–186.
Associate editor: Hiroko Nagahara