Thermochronology, Lecture 4

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Thermochronology, Lecture 4

• Analytical errors, York-fits, error chrons, U-Pb
  ages (intro), Model ages
• Mass spectrometry , Part 1

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Analytical errors

• No measurement is perfect
• Needs to be taken into account when considering
  errors on isochrons
• Precision
• Accuracy

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Acquiring data

• Tens to over a hundred individual readings of an
  isotopic ratio
• Standard error and deviation determined on the
  data set
• Some analyses that are outliers are rejected.

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A case for large errors
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Ouch
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Isochron regressions - revisited

• Take into account analytical uncertainties
• Build a regression line
• Determine MSWD

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MSWD

• MSWD Mean Square of Weighted Deviates. This is,
  roughly, a measure of the ratio of the observed
  scatter of the points (from the best-fit line) to
  the expected scatter (from the assigned errors
  and error correlations).
• T h e M S W D p a r a m e t e r c a n n o t b e c
  o m p a r e d t o t h e c l a s s i c a l R 2
  p a r a m e t e r , a n d i s n o t a m e a s
  u r e o f ho w h i g h l y c o r r e l a t e
  d t h e X - a n d Y - v a l u e s a r e .
• If the assigned errors are the only cause of
  scatter, the MSWD will tend to be near unity.
• MSWD values much greater than unity generally
  indicate either underestimated analytical errors,
  or the presence of non-analytical scatter.
• MSWD values much less than unity generally
  indicate either overestimated analytical errors,
  or unrecognized error-correlations.

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What is MSWD?

• It is the sum of the squares of the misfits of
  the regression divided by the degrees of freedom
  (number of data points minus 2).

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Example a garnet peridotite Sm-Nd age

• 3 point isochron
• Has linear fitting imperfecions and analytical
  uncertainties

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York fit

• An arbitrary procedure to deal with regression
  (lets call it geological) and analytical scatter
• It does not have physical meaning

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Pseudochrons, errorchrons

• Regression fits with scatter much larger than
  allowed by analytical - sometimes called
  errorchrons to be treated with a lot of
  caution.
• Pseudochrons- isochrons that are plain wrong.
  Usually they represent aged mixing lines.

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An example of a pseudoisochron
Hawaii peridotites
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Model ages

• For some isotopic systems, model ages are
  calculated. What are they?
• 1. Do not represent real ages of cooling or
  crystallization.
• 2. They are approximate ages of extraction of a
  material from a reservoir, such as depleted
  mantle, bulk earth, lower crust
• Give you guidelines to how old a crustal sample
  may be - was it extracted from the mantle 1 Ga, 2
  Ga, or 2 minutes ago?

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Systems that work for model age calculations

• Those whose parent daughter ratios are not
  susceptible to significant modifications
• Very incompatible (or compatible) parent element
• Those for which we have a good idea regarding
  isotopic and elemental evolution from
  nucleosynthesis through the life of the Earth

- do we know what that is?
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Example Sm-Nd

• Sm and Nd are incompatible during mantle melting
• Are robust to every day crustal processes such as
  fluid rock interaction (thus not being likely to
  modify the sm/nd of a rock)
• We have a good clue on what the Bulk Earths
  story of Sm-Nd is

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The basis of model age calcultions
Low Sm/Nd crust High Sm/Nd- mantle
We know that
Can calculate the hypothetical evolution of the
mantle as a function of time. .. And then take a
rock and find out when would it intersect that
hypothetical curve
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Example- a granite from the SW

• Say it has a crystallization age of 0.15 Ga
  (zircon U-Pb)
• However, it yields a Sm-Nd model age of 1.1. Ga
• What does it mean?

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Equations
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The rule for Nd

• About every 10 negative Epsilon units correspond
  to 1 Ga. If a whole rock sample has an ?Nd -15,
  its probably made of a material that has been
  extracted out of the mantle approximately 1.5 Ga
  ago. The rock itself can be 1 year old, and
  formed by melting an old, Precambrian lower
  crust.

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Summary

• Model ages, are reservoir extraction ages and are
  very broad indications of residence time of a
  material - not real ages
• Could be very misleading or wrong if their
  fundamental assumptions are violated (something
  that is difficult to verify).

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U-Pb, a special geochronologic system

• Will explore it in detail later
• However, need to mention that unlike the general
  solution for isochrons presented here, this
  system has some characteristics that makes it
  special
• What is it?

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U-Pb

• There are two independent isotopic clocks ticking
  at the same time (actually three but two with U
  as a parent and Pb as daughter.

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• Decay route                 t1/2,
  Byr                      Decay const., yr-1
• 238U  6  206Pb                         
  4.47                           1.55125 H 10-10
•  
•    235U  6  207Pb                         
  0.704                         9.8485  H 10-10
•  
•    232Th 6  208Pb                       
  14.01                          0.49475 H 10-10

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Equations
Do not need parent/daughter ratios
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When initial Pb is insignificant and lots of U
available.

• Such as zircon crystals
• Things get even simpler/better

Two independent systems that should yield the
same age
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Concordia diagrams

• Only U-Pb provides that kind of luxury of
  x-checking ages

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Mass spectrometry

• A brief guide through how do we get isotopic
  analyses
• What is being analyzed?
• How is it analyzed?
• How do we ensure that we get the correct answers?
• What are the differences and similarities between
  all these tools that you may have heard of TIMS,
  SIMS, ICP, MC-ICP etc?

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Today TIMS

• Stands for thermal ionization mass spectrometry
  and is by far the most used tool in heavy isotope
  measurements
• A solid sample is being uploaded onto a filament
  (Re, Ta) and heated up to over 1000 to 2000 0C at
  which T the molecules ionize in the mass spec
• The sample is being accelerated into a magnet
  equiped flight tube (which deflects various
  isotopes) and analyzed in collectors or cups at
  the end of the flight.

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Chemical separation
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Loading
Single or triple filaments, various tricks to
prevent quick sample burnout, oxidation, etc
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What is a mass spec
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Ions are counted in several collectors
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Analysis protocol

• Collect ratios
• Optimize for the radiogenic isotopic ratios
• Collect isotopic ratios that can signal
  interferences
• Collect stable isotopic ratios that can be used
  for fractionation correction - what is that?

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Isotopic fractionation

• Because the potential energy well of the bond
  involving the lighter isotope is always shallower
  than for the heavier, the bond with the lighter
  isotope is more readily broken. Hence it is
  preferentially released from the hot filament,
  causing isotopic fractionation.

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Fractionation Correction

• Luckily there are other isotopes of most elements
  of interest - stable isotopes that formed only
  during nucleosynthesis. Two such isotopes should
  always have the same ratio on Earth
• They, too, will fractionate in the mass spec the
  deviation of the measured to true value of this
  ratio is applied to the ratio of radiogenic
  isotopes
• This trick has improved the accuracies and
  precisions of isotopic ratios by hundreds of
  times.

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Example - Sr

• Four isotopes, 84, 86. 87(from 87Rb) and 88
• We measure 87/86 and do a normalization based on
  the 86/88 ratio
• Nominal 86Sr/88Sr0.1194

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Corrections

• Linear
• Power law
• Exponential
• Want to learn more bout this? - Wasserburg et al,
  1981, pdf available in library online

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Next..

• New alternatives to TIMS measurements ICP, Ion
  microprobe, etc.