Chemical Evolution across Space & Time - American Chemical Society


tional collapse of a localized dense region of an interstellar molecular cloud. ... tionation of Hf and W in the solar nebula or among different plane...
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Chapter 11

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Hafnium-Tungsten Chronometry of Planetary Accretion and Differentiation Thorsten Kleine Institute for Isotope Geochemistry and Mineral Resources, Department of Earth Sciences, ΕΤΗ Zurich, Zurich, Switzerland

The formation and earliest history of many planetary bodies in the inner solar system involved heating and melting of plane­ tary interiors, causing differentiation into silicate mantles and metal cores. A record of these earliest stages of planetary evo­ lution is preserved in the W isotopic composition of meteorites as well as lunar and terrestrial rocks. Hafnium-tungsten chronometry reveals that the early thermal and chemical evolu­ tion of asteroids is controlled by the decay of Al. This nu­ clide was sufficiently abundant to melt early-formed planetesimals (iron meteorite parent bodies) but could not raise the temperatures in the late-formed chondrite parent as­ teroids high enough to cause differentiation. Larger bodies such as the Earth grew over longer timescales and the energy required for differentiation was mainly delivered by large im­ pacts. Formation of the Earth was largely completed by the impact of a Mars-sized body that led to the formation of the Moon between 4.53 and 4.47 billion years ago. 26

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© 2008 American Chemical Society Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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Planetary Accretion and Core Formation The starting place for the accretion of the Earth and other planetary bodies is the solar nebula. This circumstellar disk of gas and dust formed by the gravitational collapse of a localized dense region of an interstellar molecular cloud. Within the inner region of the solar nebula, dust grains collide and stuck together to form a large population of meter- to kilometer-sized objects. Gravity and gas drag causes these planetesimals to collide and form increasingly larger bodies in a period of runaway growth, the products of which include numerous Moon- to Mars-sized planetary embryos. Collisions among these bodies mark the late stages of accretion culminating in the formation of a few terrestrial planets that sweep up all the other bodies. The Moon probably formed during this period, and involved a 'giant impact of a Mars-sized body with Earth at the very end of Earth's accretion (1). Planetary accretion is intimately linked with heating and subsequent melting of the planetary interiors. As a consequence, all major bodies of the inner solar system and also many smaller bodies are chemically differentiated into a metallic core and a silicate mantle. Presumably the planetary embryos began as relatively homogeneous objects, similar to the undifferentiated planetesimals observed today. However, the decay of short-lived radioactive isotopes, especially A1 (ti/ =0.73 Myr), caused the planetary interiors to heat up (2). Furthermore, collisions among the planetary embryos resulted in temperature increases during growth. At some critical size, melting will have started within the planetary embryo, causing separation and segregation of a metallic core (3). Whether or not a planetary object differentiated, however, does not only depend on its size but also on the time of its accretion. For instance, the largest asteroid Ceres (diameter = 913 km) remained undifferentiated, whereas smaller asteroids like Vesta (diameter = 512 km) underwent widespread melting and core formation. As will be discussed in more detail below, this most likely reflects differences in the time of accretion and hence the amount of A1 present at the time of accretion (2, 4-6) Melting in the interior of a planetary object permits the denser components to migrate towards the center, thereby forming a core. Metallic iron melts at lower temperatures as silicates, such that core formation occurs either by migration of molten metal through solid silicate matrix or by separation of metal droplets from molten silicate. The latter process probably is appropriate for core formation in Earth, where giant impacts cause the formation of widespread magma oceans. Once differentiation begins it proceeds rapidly. The downward motion of dense metal melts results in the release of potential energy and hence further heating, which further triggers differentiation (J). The segregation of dense, Fe-rich alloy from Mg-rich silicates causes a strong chemical differentiation of a planet. Those elements that preferentially 1

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Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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210 partition into metal (the so-called 'iron-loving' or siderophile elements) will be concentrated in the core, whereas elements with a strong affinity to silicates (the so-called 'silicate-loving' or lithophile elements) will be concentrated in the mantle. Owing to this elementalfractionationthe chemical composition of a bulk differentiated planet cannot be measured directly but it can be inferred by studying chondrites. These meteorites derive from asteroids that stayed undifferentiated. The relative abundances of elements having a high condensation temperature (the so-called refractory elements) are more or less constant among the chondrites. It is therefore assumed that almost all planetary objects of the inner solar system have chondritic relative abundances of refractory elements (the Moon is an important exception because of its overall depletion in siderophile elements). In contrast, elements having relatively low condensation temperatures (the so-called volatile elements) are stronglyfractionatedamong the chondrite parent asteroids and other planetary objects.

Hf-W Chronometry of Planetary Accretion and Differentiation

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The Extinct H f - W System l82

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The decay of H f to W is well suited to date core formation in planetary objects mainly for three reasons. First, owing to the H f half-life of ~9 Myr, detectable W isotope variations can only be produced in the first -60 Myr of the solar system. This timescale is appropriate for the formation of the Earth and Moon in particular and to planetary accretion and differentiation in general. Second, both Hf and W are refractory elements such that there is only limited fractionation of Hf and W in the solar nebula or among different planetary bodies (see above). The H f W ratio of the bulk Earth therefore can be assumed to be chondritic and hence can be measured today. Third, Hf is a lithophile and W is a siderophile element such that the chondritic H f W ratio of the Earth is fractionated internally by core formation. If core formation took place during the effective lifetime of Hf, the metal core (HffW-O) will develop a deficit in the abundance of W whereas the silicate mantle, owing to its enhanced Hf/W, will develop an excess of W (7-9). The abundance of W at time t can be subdivided in an initial component (i.e., W atoms present at the time the sample formed) and a radiogenic component (i.e., W atoms produced by H f decay after formation of the sample): 182

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I82

I82

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(D

Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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18Z

where ( W)j is the abundance of W at the time a sample formed and ( W)* is the amount of W produced by radioactive decay of Hf. The radiogenic W component is given by: 182

( Ψ)* = ( 182

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l82

1 8 2

Η^-(

Ι 8 2

Η4

(2)

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where ( Hf)i is the abundance of H f at the start of the solar system (i.e., 4567.2±0.6 (10) or 4568.5±0.5 (77) million years (Ma) ago) and ( Hf) is the abundance of H f at the time a sample formed. The number of radioactive H f atoms that remain at any time t of an original number of atoms ( Hf)i is given by: 182

t

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(

, 8 2

Hf) =(

1 8 2

t

Hf),.xe-

A t

(3)

1

where Â=0.07& Myr' is the decay constant. From equations 1 to 3 it follows: 82

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(> w) = ( w ) + ( Hf ) χ (l - e"* )

(4)

t

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Equation 4 can be modified by dividing each term by the number of W atoms, which is constant because this isotope is stable and not produced by the decay of a naturally occurring isotope of another element: (

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w

( 182

Hf

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w

+



t

i

ν

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(5)

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At the present day all H f had decayed to W and the present-day value of Hf/ W is 0, such that this ratio is replaced by ( Hf/ Hf) χ ( Hf/ W): ,82

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w W

+ 7

, 8 2

( 180

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yi

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Hf

w

180

A t

jx(l-e- )

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(6)

M

Owing to the short half-life of Hf, the present-day Value of e ~0, and it follows: ( 182

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w

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( Hf

1 8 0

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Hf ^

w

Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

(7)

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In a plot of W / W vs. H# W samples that formed from a common reser­ voir at the same time but have different Hf7 W ratios will plot on a line (the isochron) whose slope corresponds to the H f H f at the time of formation. Due to the small variations observed in nature, W isotope ratios are usually reported in 8 units, which are defined as follows: 180

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1 8 2

180

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W

WH

f(»wrw; ι x l O ("w/-wL '

For modeling purposes it is useful to express the relative to the chondritic value: i82

Ae (t) = w

(8)

W/ W of a reservoir

i84

( w/ w); i82

4

xlO

-1

4

,84

( w/ w);CHUR

(9)

Figure 1 illustrates how the Hf-W system can be used to date core forma­ tion. Tungsten isotope evolution curves are shown for the mantles and cores of three planetary bodies that underwent core formation at 10, 30, and 50 Myr, re­ spectively. As expected, an early core formation will result in larger W anomalies than a late core formation. If core formation occurred more than -50 Myr after the beginning of the solar system, no resolvable W isotope variation would evolve because most H f would have already decayed away. An age of core formation can be determined by calculating the time at which the mantle or core had the same W / W ratio than chondrites. The following equation is obtained by equating equation 7 for a reservoir j (i.e., mantle or core) and chondrites (which are representative for the W isotope evolution of the bulk planet) and combining this with equation 3: 1 8 2

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^ 1 , t=-xln λ

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/ 180

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Hf ^ 180 Hf

Hf^l

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w

( 180

Hf

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w 184

w

w

CHUR

(10)

CHUR

where CHUR denotes Chondritic Uniform Reservoir. Equation 10 illustrates the importance of the Hf-W systematics of chondrites for calculating core formation

Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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1

12

1

1

1

1

10

1

1

1

1

1

1

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1

I

/

I

I

.

ι

Chondrites (HfMM) Mantle (Hf/W~20) Core (Hf/W~0)

/ /

ω

0

J , , • • • • • •

20

40

, I , , , , I . . . , J 60

80

100

Time (Myr) Figure 1. W isotope evolution in chondrites as well as mantle and core of a differentiated planet. Shown are hypothetical core formation events at 10, 30, and 50 Myr. For the 50 Myr event the evolution curve for the core is close to zero and not shown here. Note that the As of chondrites is always zero. The W/ W ratio of the metal core does not change over time but its As value evolves to more negative values over time (equation 9). Note the differences in W anomalies that would develop depending on the time of core formation. w

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m

w

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Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

214 ages. Chondrites represent the W isotope evolution of the bulk planet and as such the reference for Hf-W core formation ages. The W isotope evolution of chondrites is defined by their present day W/ W, their H f W ratio ( Hf/ W=1.14 χ miW) and the initial Hf/ Hf of the solar system. 182

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Hf-W Evolution of Chondrites The first W isotope data for chondrites were presented by Lee and Halliday (1995, 1996) and were found to be identical to the terrestrial standard. In 2002, however, three groups independently showed that chondrites exhibit a small but resolvable W deficit relative to the terrestrial standard (12-14). Figure 2 sum­ marizes Hf-W data for chondrites and their components that define the HfW evolution of chondrites. l82

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Figure 2. Hf-W data for chondrites and their components. The present-day W/ Wand Hf/ W of the solar system is based on data from (12-14). The initial Hf/ Hf and W/ W ratios of the solar system are defined by the Hf-W isochron for CAIs. Note that the age difference between the Ste. Marguerite and CAI isochrons is consistent with the age difference between these two samples obtainedfrom Pb-Pb systematics. Hf-W data for Ste. Margueritefrom(12) andfor CAIsfrom(5, 14). 182

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m

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Zaikowski and Friedrich; Chemical Evolution across Space & Time ACS Symposium Series; American Chemical Society: Washington, DC, 2008.

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1S4

Equation 7 illustrates that in a plot of W / W vs. Hf/ W the slope of a linear regression corresponds to the Hf/ Hf at the time of formation. Thus, using a Hf-W isochron for a sample of independently known age, the Hf/ Hf at the start of the solar system can be calculated. The most direct approach to determine this value is to obtain a Hf-W isochron for Ca-Al-rich inclusions (CAIs) because these are the oldest objects that formed in the solar system. Their absolute age is usually taken as the age of the solar system. Hafnium-tungsten data for Allende CAIs define the initial Hf/ Hf of the solar system as (1.07±0.10)xl0" (5). The ordinary chondrite Ste. Marguerite has been dated with the Mn- Cr and Pb- Pb methods to be 3-4 Myr younger than CAIs (11, 15). The H# H f obtained for Ste. Marguerite (16) is lower than the Hf7 Hf of CAIs, indicating an age difference of 3.0± 1.3 Myr (calculated us­ ing equation 2). This is consistent with ages obtained from the Mn- Cr and Pb- Pb methods. Based on these data the solar system initial Hf/ Hf is well constrained to be ~1 χ 10" and hence clearly lower than an earlier estimate of -2.75 χ 10" (77). l80

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Model Ages for Instantaneous Core Formation Once the W isotope evolution of chondrites is defined, the core formation age of a planetary body can be calculatedfromthe W / W and Hf7W ratios of its core or mantle (equation 10). Samples from the metal cores and silicate man­ tles from several differentiated bodies are available in the meteorite collections, such that core formation ages can be obtained for a range of different objects including several asteroids, Mars, the Moon and Earth. 182

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Iron meteorite parent bodies Magmatic iron meteorites are thought to be samples from the metal cores of differentiated asteroids (18) and as such are ideally suited for application of HfW chronometry. Iron meteorites contain virtually no Hf (i.e., Hf7W~0), such that the timing of core formation in their parent bodies can be calculated from their W / W alone. Tungsten isotope data are now available for a vast number of iron meteorites and their W / W ratios are similar to or slightly lower than the initial W / W of Allende CAIs. Taken at face value this would indicate that core formation in the iron meteorite parent bodies predated the formation of CAIs but the W isotope composition of many iron meteorites has been altered due to prolonged exposure to cosmic rays. The interaction with thermal neutrons produced by the cosmic rays affects the W isotopes to varying degrees because their neutron capture cross sections for thermal neutrons are different. Model 182

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calculations show that the W / W ratio of iron meteorites will decrease with an increasing thermal neutron flux (Figure 3). Iron meteorites with the longest exposure times have the lowest W / W ratios, indicating that W / W ratios lower than the initial value for Allende CAIs reflect W burnout (Figure 3). Tungsten isotope data nevertheless permit dating of core formation in their par­ ent bodies, either by correcting for the effects of W burnout or by choosing samples having short exposure times. Hafnium-tungsten ages for iron meteorites indicate that core formation in their parent bodies occurred within the first -1.5 Myr of the solar system (5, 19, 20) and hence predated the formation of chondrules and chondrite parent bodies, which occurred between -2 and ~5 Myr after the formation of CAIs [based on Al-Mg and Pb-Pb ages for chondrules (10, 21, 22)]. l82

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