Description Usage Arguments Details Value References See Also Examples

View source: R/fissiontracks.R

Determines the zeta calibration constant of a fission track dataset (EDM or LA-ICP-MS) given its true age and analytical uncertainty.

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`x` |
an object of class |

`tst` |
a two-element vector with the true age and its standard error |

`exterr` |
logical flag indicating whether the external uncertainties associated with the age standard or the dosimeter glass (for the EDM) should be accounted for when propagating the uncertainty of the zeta calibration constant. |

`update` |
logical flag indicating whether the function should return an updated version of the input data, or simply return a two-element vector with the calibration constant and its standard error. |

`sigdig` |
number of significant digits |

The fundamental fission track age is given by:

*t = \frac{1}{λ_{238}}
\ln≤ft(1 + \frac{λ_{238}}{λ_f} \frac{2 N_s}{[^{238}U]A_sL}\right)
* (eq.1)

where *N_s* is the number of spontaneous fission tracks
measured over an area *A_s*, *[^{238}U]* is the
*^{238}*U-concentration in atoms per unit volume,
*λ_f* is the fission decay constant, *L* is the
etchable fission track length, and the factor 2 is a geometric
factor accounting for the fact that etching reveals tracks from
both above and below the internal crystal surface. Two analytical
approaches are used to measure *[^{238}U]*: neutron activation
and LAICPMS. The first approach estimates the
*^{238}*U-concentration indirectly, using the induced fission
of neutron-irradiated *^{235}*U as a proxy for the
*^{238}*U. In the most common implementation of this approach,
the induced fission tracks are recorded by an external detector
made of mica or plastic that is attached to the polished grain
surface (Fleischer and Hart, 1972; Hurford and Green, 1983). The
fission track age equation then becomes:

*t = \frac{1}{λ_{238}}
\ln≤ft(1 + \frac{λ_{238}ζρ_d}{2}\frac{N_s}{N_i}\right)
* (eq.2)

where *N_i* is the number of induced fission tracks counted in
the external detector over the same area as the spontaneous tracks,
*ζ* is a ‘zeta’-calibration factor that incorporates both
the fission decay constant and the etchable fission track length,
and *ρ_d* is the number of induced fission tracks per unit
area counted in a co-irradiated glass of known
U-concentration. *ρ_d* allows the *ζ*-factor to be
‘recycled’ between irradiations.

LAICPMS is an alternative means of determining the
*^{238}*U-content of fission track samples without the need for
neutron irradiation. The resulting U-concentrations can be plugged
directly into the fundamental age equation (eq.1). but this is
limited by the accuracy of the U-concentration measurements, the
fission track decay constant and the etching and counting
efficiencies. Alternatively, these sources of bias may be removed
by normalising to a standard of known fission track age and
defining a new ‘zeta’ calibration constant *ζ_{icp}*:

*
t = \frac{1}{λ_{238}}
\ln≤ft( 1 + \frac{λ_{238}ζ_{icp}}{2} \frac{N_s}{[{}^{238}U] A_s} \right)
*(eq.3)

where *[{}^{238}U]* may either stand for the
*^{238}*U-concentration (in ppm) *or* for the U/Ca (for
apatite) or U/Si (for zircon) ratio measurement (Vermeesch, 2017).

an object of class `fissiontracks`

with an updated
`x$zeta`

value

Fleischer, R. and Hart, H. Fission track dating: techniques and problems. In Bishop, W., Miller, J., and Cole, S., editors, Calibration of Hominoid Evolution, pages 135-170. Scottish Academic Press Edinburgh, 1972.

Hurford, A. J. and Green, P. F. The zeta age calibration of fission-track dating. Chemical Geology, 41:285-317, 1983.

Vermeesch, P., 2017. Statistics for LA-ICP-MS based fission track dating. Chemical Geology, 456, pp.19-27.

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