ESS 109C Isotope Geochemistry Notes

April 18, 2007

 

Mass spectrometry & Isochrons

 

  1. Class notes & homeworks are now available online –
                            http://www2.ess.ucla.edu/~schauble/Isotope_geochemistry/
  2. 2nd homework will be due next Monday (4-23-07).
    I will be traveling Thursday afternoon – Sunday, email for help.

  3. Mass spectrometry
    1. Abundances of parent and daughter nuclei are typically measured via mass spectrometer
      mass spectrometer cartoon here
    2. Key principles:

                                                     i.     Sample is ionized and accelerated by applying a voltage (analogous to electron acceleration in TV tube).

                                                      ii.     Ion beam is passed through a perpendicular magnetic field, inducing a force on the beam F = ev X B

                                                        iii.     for a beam with fixed accelerating voltage,
KE = 1/2emv2 ˆ v = sqrt(2Ve/m)

thus F = e(sqrt(2Ve/m)) X B = ma = mv2/r

                                                       iv.     r = mv2/F = m(2Ve/m)/(e(sqrt(2Ve/m)) X B)

 = 2V/(sqrt(2Ve/m)) X B) = sqrt(2Vm/e)/B

                                                      v.     Thus the path of the ion is controlled by the accelerating voltage, the perpendicular magnetic field, and its mass/charge ratio.

                                                       vi.     Throughput will be controlled by abundance, and by the ease of ionization of the atoms

1.     Widely variable between elements.

2.     Almost identical for isotopes of the same element

3.     Mass spectrometers best at determining isotope RATIOS.

4.     Isotope geochemists almost always work with isotope ratios, rather than bulk elemental/isotopic abundances.

  1. Isochron dating (87Rb/87Sr)
    1. The initial abundance of daughter nuclei in a well-mixed system can be determined if it subsequently fractionated, using the isochron method.

                                                     i.     D* =  N(exp( lt) – 1) = D – D0

D =  N(exp( lt) – 1) + D0

                                                      ii.     Convert to isotope ratio (relative to a stable daughter)
D/S =  N/S(exp( lt) – 1) + D0/S

                                                        iii.     System must be isotopically uniform, then differentiate, then close.

                                                       iv.     87Rb/87Sr: N = 87Rb (t1/2 = 48.8 Ga)
D = ?;  S = ?

                                                      v.     Imagine a crystallizing granite magma blob, that forms
Plagioclase feldspar     CaAl2Si2O8 §> NaAlSi3O8
Alkaline feldspar         KAlSi3O8
Biotite                          KMg3AlSi3O10(OH)2
Quartz                         SiO2

                                                       vi.     Which phase contains strontium?

                                                         vii.     Which phase contains rubidium?

                                                          viii.     When the magma crystallizes, what is the N/S in each phase?

                                                        ix.     What is the D/S?

                                                      x.     Isochron: D/S =  N/S(exp( lt) – 1) + D0/S     ˆ y = mx +b

1.     all minerals have same D0/S, same age (same (exp( lt) – 1)

2.     analyses of minerals will form linear array

1.     slope dependent on age (m = exp( lt) – 1)

                                                        xi.     intercept dependent on initial concentration of daughter (b = D0/S)