## Geochronology

Many elements have isotopes that are unstable, decaying to a stable isotope in a well-defined period of time. The radioactive element is called the parent element while the stable decay product is called the daughter element. The amount of daughter element at any point in time depends on the original amount of the daughter element, the original amount of the parent element, the rate at which the parent decays into the daughter element (given by the decay constant, k), and the amount of time that has elapsed. If N is the number of parent atoms in the sample, then the change in the number of those atoms over time (dN/dt) is given by dN

Integrating this gives

in which N0 is the number of parent atoms at t = t0 and Nt is the number of parent atoms remaining after time (t - t0). Nt is related to N0 and the amount of daughter element (Dr) which has been produced by the decay:

If the entire daughter element present in the sample is from the decay of the parent, then Nt and Dr will be the measurable amounts of the parent and daughter in the sample, respectively. The value of N0, the original amount of the parent, cannot be directly determined from the sample analysis, so we substitute Eq. (2.3) into Eq. (2.2) to eliminate N0:

We can rewrite Eq. (2.4) as a ratio of the daughter and parent concentrations at time t:

The amount of time for half of the original amount of the parent radioisotope to decay into the daughter is called the half-life (t1/2). It is obtained by setting Nt = 1/2 N0 in Eq. (2.2), which then reduces to

Thus, the decay constant, k, and the half-life, t1/2, are related to each other by k=0693. (2.7)

t1/2

Igneous rocks typically contain small amounts of radioactive elements and are therefore the most useful rocks for geochronologic purposes. Some of the common radioisotope systems used in geologic analysis are given in Table 2.1.

Equation (2.5) can provide the age of an individual sample for which the concentrations of the daughter and parent elements are measured. However, the uncertainties in ages based on a single measurement are typically quite large. Geochemists therefore determine a rock's age from measurements of several minerals within the sample. The resulting age is the crystallization age of the sample, which indicates the amount of time that has elapsed since the rock solidified.

The amount of the daughter element at some time t (Dt) is the sum of the original amount of daughter at t = to (Do) and the amount which has been produced by the decay of the parent (Dr):

Thus, we also need to know the initial (non-radiogenic) amount of daughter to uniquely determine the crystallization age of the sample. While absolute

Differentiation and core formation Table 2.1 Geologically important radionuclides

Parent

Daughter

Half-life (yrs)

106x109 48.8x109

103x106 82xl06 17x106 9x106 3.6x106 7.2x105

46x109 14x109

4.47 x109 1.25 x109 7.04x108

concentrations are impossible to determine, the ratio of the daughter isotope to another isotope of the same element which is not produced by radioactive decay is typically a constant for material formed from a particular region of the solar nebula. If we represent this stable isotope of the daughter element by X, the left side of Eq. (2.5) becomes

The ratio D0 /X is constant for all mineral samples and will drop out when comparing the concentrations of Dt/X and Nt/X among the different samples. Therefore, crystallization ages are determined using these ratios rather than absolute concentrations of parent and daughter elements.

Crystallization ages are determined using isochron diagrams, such as that shown for the rubidium (Rb)-strontium (Sr) system in Figure 2.3. Strontium-86 (86Sr) is the non-radiogenic isotope of strontium to which the 87Rb and radiogenic 87Sr are compared. Assume that at time t0 we have magma solidification occurring. Three

### 87 86

minerals in this melt (A, B, and C) have specific Rb/ Sr concentrations, as shown. While the reservoir is molten, any 7Sr produced by the decay of 7Rb is free

to migrate through the reservoir. Hence the concentration of Sr in the magma reservoir will be homogeneous. At time t0 when the magma reservoir solidifies, the concentration of 87Sr/86Sr is therefore constant, as shown in Figure 2.3. Once the

### 87 86 87 86

reservoir solidifies, the concentration of Sr/ Sr increases and that of Rb/ Sr decreases within each specific mineral due to the decay of 87Rb. The concentrations of these elements for our three minerals changes as shown by the arrows in Figure 2.3.

87Sr/86Sr t = present

87Rb/86Sr

Figure 2.3 Isochron diagram, showing how rubidium (Rb) decays into strontium (Sr) in three minerals (A, B, and C) over a time period t0 to t.

### 07 o6 87 86

At time t, we can measure concentrations of Rb/ Sr and Sr/ Sr and compare them among the three minerals. From the graph and Eq. (2.5), the slope of the isochron ("equal time") line at time t is given by

where A indicates the difference in concentrations between two minerals. This equation gives the crystallization age (t - t0) of the sample from which the minerals were obtained.

The above technique only provides accurate crystallization ages if the system has been "closed" since the reservoir solidified. A closed chemical system is one where there has been no addition or subtraction of parent and/or daughter elements. Open chemical systems are often seen when either the parent or daughter element is very volatile - an increase in temperature can cause the volatile component to readily escape from the system. To determine whether the system has been open or closed, geochemists look at the whole rock age. The isochron graph for a whole rock age

87 86 87 86

uses the average Rb/ Sr- Sr/ Sr value for the entire rock. The initial value of

87Sr/86Sr is the second point on the graph, allowing the isochron line to be drawn

### 87 86

between these two points. The initial Sr/ Sr value is determined from the oldest age measurements of Solar System material. This measurement comes from basaltic achondrite meteorites, which formed 4.5 Ga ago when the Solar System formed. The 87Sr/86Sr value from the basaltic achondrites is called the Basaltic Achondrite Best Initial (BABI) value and is equal to 0.69899 ± 0.000 04 (Birck and Allègre, 1978). The model age which results from the whole rock analysis fixes the time of origin of the initial materials comprising the rock, without regard to the rock's subsequent history. If the model age equals the age of the Solar System (4.5 Ga), the system is a

Figure 2.4 EETA 79001 is one of the shergottite martian meteorites. It was the first martian meteorite in which gas from the martian atmosphere was identified. (NASA/Johnson Space Center [JSC].)

closed system. If the model age is not equal to the age of the Solar System, the system has been an open system during at least some part of its lifetime. A model age less than the age of the Solar System indicates that the parent-to-daughter ratio (N/D) has increased while an age greater than the age of the solar system indicates that N/D has decreased.

### 2.2.3 Martian meteorites

Most meteorites have crystallization ages of 4.5 Ga and are believed to represent material which formed directly from the solar nebula. By 1979, however, three meteorites were known with younger formation ages and distinct mineralogic properties. These three meteorites were seen to fall in 1865 near Shergahti, India, in 1911 near El-Nakhla, Egypt, and in 1815 near Chassigny, France. These three meteorites are now called Shergotty, Nakhla, and Chassigny, respectively, and are the representative samples of the meteorites called the shergottites, nakhlites, and chassignites (SNC) (Figure 2.4).

By 1979, scientists began to speculate that the SNC meteorites are pieces of Mars ejected off the planet during meteorite impacts. All of the SNC meteorites are volcanic rocks and all but one have formation ages <1.35Ga. The young ages and volcanic textures indicate that these rocks come from a body where volcanism has been occurring up to at least 0.16Ga ago (age of youngest SNC). Analysis of the oxygen isotopes in these rocks revealed that they are distinct from terrestrial, lunar, and most meteoritic rocks (Clayton and Mayeda, 1996). By 1980, the circumstantial evidence strongly suggested that Mars is the parent body of the SNC meteorites. The 1982 discovery that the isotopic composition of trapped noble gases within the SNC

 Meteorite name Year found Type Crystallization age (yrs) Chassigny 1815 Chassignite 1.3X109 Shergotty 1865 Basaltic shergottite 165x10® Nakhla 1911 Nakhlite 1.3xl09 Lafayette 1931 Nakhlite 1.3xl09 Governador Valadares 1958 Nakhlite 1.3xl09 Zagami 1962 Basaltic shergottite 180x10® ALHA 77005 1977 Lherzolitic shergottite 185xl06 Yamato 793605 1979 Lherzolitic shergottite 170x10® EETA 79001 1980 Olivine-phyric and basaltic 180x10® shergottite ALH 84001 1984 Orthopyroxenite 4.1 xlO9 LEW 88516 1988 Lherzolitic shergottite 180x10® QUE 94201 1994 Basaltic shergottite 320x10® Dar al Gani 476, 489, 670, 735, 1997-1999 Olivine-orthopyroxene shergottite 474x10® 876, 915b Yamato 980459 1998 Olivine-phyric shergottite 472x10® Los Angeles 001, 002 1999 Basaltic shergottite 165x10® Sayh al Uhaymir 005, 008, 051, 1999-2004 Olivine-phyric shergottite N.d. 094, 060, 090, 120, 150fo Dhofar 019 2000 Olivine-phyric shergottite 525x10® GRV 99027 2000 Lherzolitic shergottite N.d. Dhofar 378 2000 Basaltic shergottite N.d. Northwest Africa 480, 1460fo 2000-2001 Basaltic shergottite 340x10® Yamato 000593, 000749, 000802fo 2000 Nakhlite 1.3xl09 Northwest Africa 817 2000 Nakhlite 1.35X109
 Northwest Africa 1669 2001 Basaltic shergottite N.d. Northwest Africa 1950 2001 Lherzolitic shergottite N.d. Northwest Africa 856 2001 Basaltic shergottite 186x10® Northwest Africa 1068, 1110, 2001-2004 Olivine-phyric shergottite 185xl06 1183, 1775fo Northwest Africa 998 2001 Nakhlite 1.3xl09 Northwest Africa 1195 2002 Olivine-orthopyroxene N.d. shergottite Northwest Africa 2046 2003 Olivine-orthopyroxene N.d. shergottite MIL 03346 2003 Nakhlite 1.02xl0? Northwest Africa 2737 2004 Chassignite 1.3xl09 Northwest Africa 3171 2004 Basaltic shergottite N.d. Northwest Africa 2626 2004 Olivine-orthopyroxene N.d. shergottite YA1075 ?? Lherzolitic shergottite N.d. Northwest Africa 2975 2005 Basaltic shergottite N.d. GRV 020090 2005 Lherzolitic shergottite N.d. Northwest Africa 2646 2005 Lherzolitic shergottite N.d.

a N.d., no data available. b Fragmented meteorites.

Source: Data from Mars Meteorite Compendium: curator.jsc.nasa.gov/antmet/mcc/index.cfm u->

meteorites was statistically identical to the martian atmosphere clinched the case for a martian origin of the SNC meteorites (Bogard and Johnson, 1983).

As of 2006, 37 martian meteorites are known (Table 2.2). Of these meteorites 27 are classified as shergottites, seven are nakhlites, and two are chassignites. The last meteorite is ALH84001, an orthopyroxenite which is an apparent sample of the ~4-Ga-old cumulate crust of Mars.

Shergottites are subdivided into four classes, based on composition: basaltic, lherzolitic, olivine-orthopyroxene, and olivine-phyric. Nakhlites are rich in olivine while chassignites are dunites. ALH84001 is the only orthopyroxenite among the known martian meteorites. These 37 meteorites have been shocked to various degrees (pressure range from 30 to 50GPa) and have apparently been ejected off Mars in five to eight different impact events (Nyquist et al., 2001). The timing of these ejection events can be estimated by the cosmic ray exposure ages of the meteorites - all are <16 X106 years (10 years = 1 Ma). Many different craters have been proposed as the sources of these meteorites, based on geologic analysis (Wood and Ashwal, 1981; Mouginis-Mark et al., 1992a; Barlow, 1997; Tornabene et al., 2006). Comparison of meteorite mineralogies with information from MGS TES and Odyssey THEMIS instruments has been difficult since much of the surface is covered by dust which masks the underlying mineralogy, but a few intriguing areas have been identified by this technique (Hamilton et al., 2003; Harvey and Hamilton, 2005).

One of the perplexing issues related to martian meteorites is why 97% of the meteorites come from geologically young terrains when such surfaces are believed to constitute <40% of Mars' surface area. This martian meteorite paradox was of particular concern when it was thought that all martian meteorites were ejected from a single large impact crater (Melosh, 1984) - such large impact craters are rare on younger surfaces. Although multiple impact sites are now proposed (Treiman, 1995; Nyquist et al., 2001) and smaller impacts are capable of launching the martian meteorite material (J.N. Head etal., 2002), the primary difference in surface ejection capability appears to be that the thicker regolith cover on older surfaces likely inhibits ejection of the martian meteorites from those regions (Hartmann and Barlow, 2006).

### 2.2.4 Differentiation and core formation on Mars

Martian meteorite analysis provides important constraints on the early evolution of Mars, particularly in regard to the planet's differentiation and core formation. Most of the results are based on analysis of the shergottites, which, due to their volcanic textures, provide information about mantle conditions.

Based on martian meteorite analysis, Wanke (1981) proposed that Mars accreted from two major reservoirs of material, both with chondritic (C1) abundance ratios. Component A consisted of highly reduced, volatile-poor materials while

Component B was oxidized and volatile-rich. Dreibus and Wanke (1985) argued for homogeneous accretion of these two components in a ratio of 60% Component A to 40% Component B. Planetary formation models suggest that accretion of Mars occurred rapidly, within ~0.1Ma (Wetherill and Inaba, 2000), and that Mars was largely spared from late-stage large impact events (Chambers and Wetherill, 1998) which affected the interior geochemistry of other bodies.

The addition of heat from accretion, large impacts, and short-lived radioactivity melted the planet and caused differentiation. Evidence for an early differentiation of Mars comes from analysis of 182W, the daughter product resulting from decay of 182Hf (Hf: hafnium). Tungsten (W) behaved as a siderophile element early in martian history, following iron (Fe) to the core during core formation. Any 182W produced after core formation will remain in the mantle. Since the half-life of 182Hf is 9Ma, the detection of radiogenic 182W in mantle materials provides constraints on the timing of differentiation and core formation. The Hf/W ratio is approximately

five times lower on Mars than in terrestrial materials, but some radiogenic W has been detected. The W analysis suggests that accretion and differentiation on Mars was complete within 10 to 15Ma after Solar System formation (Lee and Halliday, 1997; Kleine et al., 2002). This is supported by a correlative relationship in the behavior of neodymium (Nd) and W, suggesting that both underwent fractionation from the mantle material within the first 15Ma of Solar System history (Halliday et al., 2001). Early core formation is likewise indicated by the observation that the lead (Pb) isotopes (206Pb and 207Pb) follow the U/Pb geochron at 4.5Ga ago (Chen and Wasserburg, 1986), and that Re/Os analysis suggests early fractionation of rhenium (Re) from osmium (Os) (Brandon et al., 2000).

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