Determining the age of rocks

30
Appendix 1: Common Pb Correction
202Hg and the combination of 204Hg+204Pb are measured for purposes of
common Pb correction. In the analysis below, no fractionation is assumed for the various
isotopes; as such, the current A2Z preference is to avoid applying this correction until the
fractionation of Hg and Pb isotopes in the apparatus used is better understood. The
isotopic abundances of the Hg isotopes measured are (Friedlander et al., 1981):
202Hgfraction = 0.298
204Hgfraction = 0.069
Common Pb isotopic ratios are (Chen and Wasserburg, 1983):
206Pb/204Pbcommon = 9.3066
207Pb/204Pbcommon = 10.293
208Pb/204Pbcommon = 29.475
Common 204Pb is calculated as follows:
204Pbcommon = (204Hg204Pb) – [(204Hgfraction/202Hgfraction) * 202Hg] (if <0 for a
scan then set to 0)
Common Pb corrected isotopic ratios are calculated as follows:
206Pb = 206Pb_background_corrected – (204Pbcommon * 206Pb/204Pbcommon) (if <0
for a scan then set to 0)
207Pb = 207Pb_background_corrected – (204Pbcommon * 207Pb/204Pbcommon) (if <0
for a scan then set to 0)
208Pb = 208Pb_background_corrected – (204Pbcommon * 208Pb/204Pbcommon) (if <0
for a scan then set to 0)
©2010 Apatite to Zircon, Inc. page 31
Appendix 2: Primary Age Standard Fractionation Factor Correction for α-
Radiation Damage
Function dAlphaEnergy (below) is used to calculate the relative α-radiation
damage. Th232, U235c, and U238 represent the signal intensities for these isotopes for
the current scan. Parameters ageTh232, ageU235c, and ageU238 represent the respective
UPb ages for the current scan. Values of dAlphaEnergy are summed for all scans for a
spot.
Function dAlphaEnergy(U235c, U238, Th232, ageU235c, ageU238, ageTh232, ffage)
'dim ageU235c, ageU238, ageTh232, ffage(5) implicit
'U235c
dAlphaEnergy = (7 * 5.94 * U235c / ffage(2)) * (Exp(lamdaU235 * ageU235c) - 1)
'U238
dAlphaEnergy = dAlphaEnergy + (8 * 5.36 * U238 / ffage(3)) * (Exp(lamdaU238 * ageU238) - 1)
'Th232
dAlphaEnergy = dAlphaEnergy + (6 * 5.83 * Th232 / ffage(5)) * (Exp(lamdaTh232 * ageTh232) - 1)
End Function
Corrections of the fractionation factors for the primary age standard are
performed using the following subroutine. Several important parameters have the
following meanings:
nAgeStdPreferred1=index for the primary age standard (FC-1 in most cases)
nAgeStdPreferred2=index for the secondary age standard (TR in most cases)
StdAlphaEnergy(nAgeStdPreferred1)=relative α-radiation damage for the primary
age standard
StdAlphaEnergy(nAgeStdPreferred2)=relative α-radiation damage for the secondary
age standard
SAlphaEnergy=average StdAlphaEnergy(nAgeStdPreferred1) per scan multiplied by
the scan number i
UAlphaEnergy=sum of dAlphaEnergy values (function dAlphaEnergy) for scans 1
through i
std207235Age(nAgeStdPreferred2)=accepted 207Pb/235Uc age for the secondary age
standard (same for std208238… and std207206…)
measAgeStdPreferred2=measured age for the secondary age standard when calculated
without fractionation factor correction
Several conditional statements limit the amount of fractionation factor corrections
that are permitted. a) If UAlphaEnergy≥SAlphaEnergy then no correction is performed.
b) No fractionation factor is permitted to be set less than the minimum value observed for
the respective isotopic ratio for the primary age standard.
Sub AlphaEnergyFF(SAlphaEnergy, UAlphaEnergy, ffage, minff)
'dim ffage(5),minff(5) implicit
Dim x1, x2, y1, y21, y22, y2235, y2238, y2232, m, b
If UAlphaEnergy < SAlphaEnergy Then
'calibration for acceptable 207/206
x1 = 1 'FC-1/FC-1
x2 = (StdAlphaEnergy(nAgeStdPreferred2) / StdAlphaEnergy(nAgeStdPreferred1)) 'IFCT/FC-1
y1 = 1 'FC-1/FC-1
'235Uc
y2235 = std207235Age(nAgeStdPreferred2) / measAgeStdPreferred2
m = (y2235 - y1) / (x2 - x1)
b = y2235 - x2 * m
ffage(2) = ffage(2) * (m * UAlphaEnergy / SAlphaEnergy + b)
If ffage(2) < minff(2) Then
ffage(2) = minff(2)
End If
'238U
©2010 Apatite to Zircon, Inc. page 32
y2238 = std206238Age(nAgeStdPreferred2) / measAgeStdPreferred2
m = (y2238 - y1) / (x2 - x1)
b = y2238 - x2 * m
ffage(3) = ffage(3) * (m * UAlphaEnergy / SAlphaEnergy + b)
If ffage(3) < minff(3) Then
ffage(3) = minff(3)
End If
'232Th
y2232 = std208232Age(nAgeStdPreferred2) / measAgeStdPreferred2
m = (y2232 - y1) / (x2 - x1)
b = y2232 - x2 * m
ffage(5) = ffage(5) * (m * UAlphaEnergy / SAlphaEnergy + b)
If ffage(5) < minff(5) Then
ffage(5) = minff(5)
End If
End If
End Sub
©2010 Apatite to Zircon, Inc. page 33
Appendix 3: Functions for Calculating U-Pb Ages
The following functions are used by UPbICP to calculate U-Pb ages for their
respective isotopic ratios (input parameter ratio).
Function Age207235(ratio)
'dim ratio,Age207235 implicit
If ratio < 0 Then
Age207235 = 0
Else
Age207235 = (1 / lamdaU235) * Log(ratio + 1)
End If
End Function
Function Age206238(ratio)
'dim ratio,Age206238 implicit
If ratio < 0 Then
Age206238 = 0
Else
Age206238 = (1 / lamdaU238) * Log(ratio + 1)
End If
End Function
For 207Pb/206Pb ratios, U-Pb ages must be calculated by iteration. To avoid this, UPbICP
reads an array ratio207206_data indexed from i = 1 to 45600 and containing 207Pb/206Pb
ratios corresponding to i x 105 years for each index i.
Function Age207206(ratio)
'dim ratio,Age207206 implicit
Dim i, m, b
If ratio <= Pb207206init Or ratio > ratio207206_data(45600) Then
Age207206 = 0
Else
For i = 1 To 45600
If ratio < ratio207206_data(i) Then
m = 0.1 / (ratio207206_data(i) - ratio207206_data(i - 1))
b = CSng(i - 1) * 0.1 - ratio207206_data(i - 1) * m
Age207206 = m * ratio + b
Exit Function
End If
Next i
End If
End Function
©2010 Apatite to Zircon, Inc. page 34
Table 1. ICP-MS and laser ablations system operating conditions and data acquisition
parameters.
ICP-MS: operating
conditions
Instrument Finnigan Element II Magnetic Sector
ICP-MS
Forward power 1.25 kW
Reflected power <5 W
Plasma gas Ar
Coolant flow 15 l/min
Carrier flow 1.0 l/min (Ar) 0.8 l/min (He)
Auxiliary flow 1.0 l/min
ICP-MS: data
acquisition parameters
Dwell time 24 milliseconds per peak point
Points per peak 3
Mass window 5%
Scans 255
Data acquisition time 38.5 sec
Data acquisition mode E scanning
Isotopes measured 202Hg,204Pb,206Pb,207Pb,208Pb,232Th,235U,238U (scans ~60-250)
28Si,91Zr (scans 251-255)
Laser ablation system:
operating conditions
Laser type New Wave Neodymium: YAG
Wavelength 213 nm
Laser mode Q switched
Laser output power 10 J/cm2
Laser warm up time 6 sec
Shot repetition rate 5 Hz
Sampling scheme spot (20 μm)
©2010 Apatite to Zircon, Inc. page 35
Table 2. Age standards used at A2Z.
Standard Standard U-Pb age (±2σ) Reference
FC-1 Duluth
complex
1099.0 ± 0.6 Ma Paces and Miller, 1993
FC-5z Duluth
complex
1099.0 ± 0.6 Ma
(assumed equal to
FC-1)
Paces and Miller, 1993
TR Tardree
Rhyolite
61.23 ± 0.11 Ma Dave Chew, personal
communication
IFCan Fish
Canyon
Tuff
28.201 ± 0.012
Ma
Kuiper et al., 2008
R33 Braintree
complex
418.9 ± 0.4 Ma Black et al., 2004
TEM2 Temora 2,
Middledale
gabbroic
diorite
416.78 ± 0.33 Ma Black et al., 2004
MD Mount
Dromedary
99.12 ± 0.14 Ma Renne et al., 1998
200-01 Tioga Bed
K bentonite
391.4 ± 1.8 Ma Tucker et al., 1998
Table 3. Weighted mean U and Th ppm values assumed for FC-1 (Paces and Miller,
1993)
mg Uppm Thppm mg*Uppm mg*Thppm
125 420 258 52500 32250
120 1510 905 181200 108600
155 299 170 46345 26350
118 218 115 25724 13570
133 292 176 38836 23408
sum mg mg*Uppm/sum
mg
mg*Thppm/sum
mg
651 weighted mean 529.35 313.64