1.Introduction2.History3.Chemical properties4.Nuclear properties5.Importance of Rb-Sr dating6.Methodology for dating7.Source of Rb-Sr8.Isochron equation9.Sources of error/ limitations10.Uses11.Reference

The rubidium-strontium dating method is a radiometric dating technique used by scientists to determine the age of rocks and minerals from the quantities they contain of specific isotopes of rubidium (87Rb) and strontium ( 87Sr, 86Sr).

Development of this process was aided by German chemist Fritz Strassmann, who later went on to discover nuclear fission with German chemist Otto Hahn and Swedish physicist Lise Meitner.

Rubidium Alkali element (group

I) +1 valency Ionic radii 1.48

angstrom which is close to “K” so it substitute for K e.g. in K-feldspar and mica.

More incompatible Its concentration is

high in crust then in mental.

Strontium Alkaline earth element

(group II A) +2 valency Ionic radii 1.13

angstrom which is close to Ca, so Sr can replace it in Ca containing minerals like in plagioclase and CPX.

Less incompatible than Rb

Its concentration in crust is less than Rb.

Rb is a highly incompatible element. Sr is fairly incompatible.

This means that as partial melting occurs, Rb is going to partition to the melt in greater proportion than Sr will.

From this partitioning, the mantle will become depleted in Rb relative to Sr and is called depleted mantle.

Concurrently, the crust will become enriched in Rb relative to Sr.

Atomic mass no. Rubidium abundance(%)

Strontium abundance(%)

84 ------------------ 0.56 (stable)

85 72.12 (stable) -----------------

86 ------------------- 9.87 (most stable)

87 27.83 (unstable) 7.00 (stable)

88 ------------------- 82.57 (stable)

The element rubidium consists of two isotopes having atomic mass numbers of 85 (72.16%) and 87 (27.84%).

Rb decays to 87Sr by a weak b- emission.  The decay constant is :- l = 1.42 x 10-11 /yr.

Rubidium-87 decays to Strontium-87 by beta decay according to the above equation.

The amount of 87Sr found in a sample at any time is determined by:-

1. the decay constant of  87Rb, 2.the initial amount of 87Sr in the sample,3. the time since the initial time and the

ratio of Rb to Sr in the system. 4.This can be seen in the equation below.

Where lambda is the decay constant and t is the age of the system.

The utility of the rubidium-strontium isotope system results from the fact that :-

•  87Rb (one of two naturally occurring isotopes of rubidium) decays to 87Sr with a half-life of 48.8 billion years.

• Rb is a highly incompatible element that, during fractional crystallization of the mantle, stays in the magmatic melt rather than becoming part of mantle minerals.

• The radiogenic daughter, 87Sr, is produced in this decay process and was produced in the original primordial nucleosynthesis of the universe.

Different minerals gives different ratios of radiogenic strontium-87 to naturally occurring strontium-86 (87Sr/86Sr) through time; and their age can be calculated by:-

1.measuring the 87Sr/86Sr in a mass spectrometer,

2.knowing the amount of 87Sr present when the rock or mineral formed,

3.and calculating the amount of 87Rb from a measurement of the Rb present

4.and knowledge of the 85Rb/87Rb weight ratio.

If these minerals crystallized from the same silicic melt, each mineral had the same initial 87Sr/86Sr as the parent melt. However, because Rb substitutes for K in minerals and these minerals have different K/Ca ratios, the minerals will have had different Rb/Sr ratios.

During fractional crystallization, Sr tends to become concentrated in plagioclase, leaving Rb in the liquid phase.

Hence, the Rb/Sr ratio in residual magma may increase over time, resulting in rocks with increasing Rb/Sr ratios with increasing differentiation.

Typically, Rb/Sr increases in the order:- plagioclase, hornblende, K-feldspar, biotite, muscovite.

Therefore, given sufficient time for significant production (ingrowth) of radiogenic 87Sr, measured 87Sr/86Sr values will be different in the minerals, increasing in the same order.

Consider the case of an igneous rock such as a granite that contains several major Sr-bearing minerals including plagioclase feldspar, K-feldspar, hornblende, biotite, and muscovite.

Each of these minerals has a different initial rubidium/strontium ratio dependent on their potassium content, the concentration of Rb and K in the melt and the temperature at which the minerals formed.

Rubidium substitutes for potassium within the lattice of minerals at a rate proportional to its concentration within the melt.

The ideal scenario according to Bowen's reaction series would see a granite melt begin crystallizing a cumulate assemblage of plagioclase and hornblende (i.e.; tonalite or diorite), which is low in K (and hence Rb) but high in Sr (as this substitutes for Ca), which proportionally enriches the melt in K and Rb.

This then causes orthoclase and biotite, both K rich minerals into which Rb can substitute, to precipitate.

The resulting Rb-Sr ratios and Rb and Sr abundances of both the whole rocks and their component minerals will be markedly different.

This, thus, allows a different rate of radiogenic Sr to evolve in the separate rocks and their component minerals as time progresses.

The age of a sample is determined by analyzing several minerals within the sample.

The 87Sr/86Sr ratio for each sample is plotted against its 87Rb/86Sr ratio on a graph called an isochron.

If these form a straight line then the samples are consistent, and the age probably reliable.

The slope of the line dictates the age of the sample.

87Rb decays to 87Sr* by b decay. The neutron emits an electron to become a proton.

For this decay reaction, l = 1.42 x 10-11 /yr,  t1/2 = 4.8 x 1010 yr

At present, 27.85% of natural Rb is 87Rb. If we use this system to plug into equation,

D* = Nelt-N  =  N(elt-1) then, 87Sr* = 87Rb (elt-1)         (1.)but, 87Srt = 87Sr0 + 87Sr*

Plugging this into equation (1)

87Srt = 87Sr0 + 87Rb (elt-1)    (2)

We still don't know 87Sr0 , the amount of 87Sr daughter element initially present.

To account for this, we first note that there is an isotope of Sr, 86Sr, that is:(1)  non-radiogenic (not produced by another radioactive decay process),(2)  non-radioactive (does not decay to anything else).Thus, 86Sr is a stable isotope, and the amount of 86Sr does not change through timeIf we divide equation (2) through by the amount of 86Sr, then we get:-

(87Sr/86Sr) t = (87Sr/86Sr ) 0+(87Rb/86Sr)

t(elt -1)

Since, it is a lot easier to measure the ratio of isotopes in a sample of rock or a mineral, rather than their absolute abundances. Therefore we divide the above equation by Sr86

The above equation is known as

“ISOCHRON EQUATION”.

We can measure the present ratios of (87Sr/86Sr)t and (87Rb/86Sr)t with a mass spectrometer, thus these quantities are known.The only unknowns are thus (87Sr/86Sr)0 and t. Note also that isochron equation has the form of a linear equation, i.e.

y = mx +bwhere b, the y intercept, is (87Sr/86Sr)0 and m= the slope is (elt -1) and x is (87Rb/86Sr)t  

First note that the time  t=0 is the time when initial value of 87Sr/86Sr was the same in every mineral in the rock (such as at the time of crystallization of an igneous rock) because at magmatic temperature, there will be no fractionation. So y remains constant and there will be change in x-axis. In nature, however, each mineral in the rock is likely to have a different amount of87Rb. So that each mineral will also have a different 87Rb/86Sr ratio at the time of crystallization. It decreases with passage of time whereas (87Sr/86Sr) increases with time Thus, once the rock has cooled to the point where diffusion of elements does not occur, the 87Rb in each mineral will decay to87Sr, and each mineral will have a different 87Rb and 87Sr after passage of time.

After a passage of time, a new rock is formed and it will inherit (87Sr/86Sr). Whatever initial (87Sr/86Sr)

was there, that was inherited by arbitrary.

(87Sr/86Sr) will keep on increasing because of the continuous decay of Rb-87.

Sr will contain both original and inherited along with radiogenic.

1. After each period of time, the 87Rb in each rock decays to 87Sr producing a new line.

2. This line is still linear but is steeper than the previous line.

3. We can use this to tell us two important things1. The age of the rock2. The initial 87Sr/86Sr isotope ratio

It tells the source from which this particular rock is obtained.

Cut-off limit is 0.706. Rock is crustal if >0.706 Rock is mantle if <0.706

If samples are clustered then we can’t get the value of isochron.

There should be large variation between Rb isotope.

There should be large spread in Rb/Sr ratio i.e high and low value.

If initial ratio is not uniform then also we don’t get isochron. So, composition of daughter must be homogenous when a new rock is formed.

Rb and Sr are mobile elements. Any rock which is slightly altered, these elements will leach out.

In this case, we get younger age i.e wrong age than actual age.

Since basaltic rock has more alteration as compare to granitic rock so they are not preferred.

So mostly mantle derived rocks would not generate a good Rb-Sr isochron.

The figure to the left shows an isochron defined by the data points from analyses of five samples of granite from a single pluton.

The necessary  conditions for the isochron are that at some time all samples had the same 87Sr/86Sr ratio, and that since that time, all samples have remained closed systems with respect to Rb and Sr.

The slope of the isochron

(.0057158) corresponds to a time of 401.7 million years, and the intercept indicates that, at that time all samples had a 87/86 ratio of 0.70382.

The figure at left is a hypothetical 87Sr/86Sr growth curve for the mantle prior to formation of continental crust and, crust and mantle growth curves after crustal formation.  The steeper crustal growth curve is due to the higher Rb/Sr ratio in the crust, and crustal extraction depleted the mantle in its Rb/Sr ratio resulting in slower growth of 87Sr/86Sr.

Rb-Sr dating relies on correctly measuring the Rb-Sr ratio of a mineral or whole rock sample, plus deriving an accurate 87Sr/86Sr ratio for the mineral or whole rock sample.

Several preconditions must be satisfied before a Rb-Sr date can be considered as representing the time of emplacement or formation of a rock.

The system must have remained closed to Rb and Sr diffusion from the time at which the rock formed or fell below the closure temperature i.e  the temperature at which a system has cooled so that there is no longer any significant diffusion of the daughter isotopes out of the system and into the external environment (generally considered to be 650 °C);

The minerals which are taken from a rock to construct an isochron must have formed in chemical equilibrium with one another or in the case of sediments, be deposited at the same time;

The rock must not have undergone any metasomatism (i.e. the chemical alteration of a rock by hydrothermal and other fluids) which could have disturbed the Rb-Sr system either thermally or chemically

One of the major drawbacks of utilizing Rb and Sr to derive a radiometric date is their relative mobility, especially in hydrothermal fluids. Rb and Sr are relatively mobile alkaline elements and as such are relatively easily moved around by the hot hydrothermal fluids present during metamorphism.

Conversely, these fluids may metasomatically alter a rock, introducing new Rb and Sr into the rock. Rb-Sr can then be used on the altered mineralogy to date the time of this alteration, but not the date at which the rock formed.

Uses of Rb-Sr Dating

geochronologyIsotope

geochemistry

Strontium Isotope

stratigraphy

If the initial amount of Sr is known or can be extrapolated, the age can be determined by measurement of the Rb and Sr concentrations and the 87Sr/86Sr ratio. The dates indicate the true age of the minerals only if the rocks have not been subsequently altered.

The important concept in isotopic tracing is that Sr derived from any mineral through weathering reactions will have the same 87Sr/86Sr as the mineral.

Geochronology

Initial 87Sr/86Sr ratios are a useful tool in archaeology, forensics and paleontology because the 87Sr/86Sr of a skeleton, sea shell or indeed a clay artifact is directly comparable to the source rocks upon which it was formed or upon which the organism lived. Thus, by measuring the current-day 87Sr/86Sr ratio, the geological fingerprint of an object or skeleton can be measured, allowing migration patterns to be determined.

Strontium isotope stratigraphy relies on recognized variations in the 87Sr/86Sr ratio of seawater over time. The application of Sr isotope stratigraphy is generally limited to carbonate samples for which the Sr seawater curve is well defined. This is well known for the Cenozoic time-scale but, due to poorer preservation of carbonate sequences in the Mesozoic and earlier, it is not completely understood for older sequences.

In older sequences diagenetic alteration combined with greater uncertainties in estimating absolute ages due to lack of overlap between other geochronometers (for example U-Th leads to greater uncertainties in the exact shape of the Sr isotope seawater curve.

Jacobsen S.B., Wills J., Yin Q., 2000. Seawater isotope records, crustal evolution, tectonics and atmospheric evolution. Proceedings, Seventh Annual V.M. Goldschmidt Conference, 2000. PDF abstract

USGS (2004) Resources on Isotopes:Strontium, http://wwwrcamnl.wr.usgs.gov/isoig/period/sr_iig.html.

Attendorn, H. -G.; Bowen, Robert (1988). "Rubidium-Strontium Dating". Isotopes in the Earth Sciences. Springer. pp. 162–165. http://books.google.de/books?id=k90iAnFereYC&pg=PA162.

Walther, John Victor (1988 2009). "Rubidium-Strontium Systematics". Essentials of geochemistry. Jones & Bartlett Learning. pp. 383–385. http://books.google.de/books?id=cYWNAZbPhMYC&pg=PA383

ISOTOPE GEOLOGY by ‘CLAUDE.J.ALLEGRE’.. The Cambridge Publication UNITED KINGDOM.

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