Mathematics – Logic
Scientific paper
May 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991gecoa..55.1449c&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 55, Issue 5, pp.1449-1465
Mathematics
Logic
33
Scientific paper
Annealing of etchable fission-track damage in fluorapatite (Ca 4.96 Fe 0.01 Na 0.02 Sr 0.01 REE 0.01 ) 5.01 -(P 2.98 Si 0.02 ) 3.00 O 12 (F 1.00 Cl 0.02 ) 1.02 and Sr fluorapatite (Ca 4.68 Na 0.04 Sr 0.02 REE 0.03 ) 4.97 (P 2.98 Si 0.03 ) 3.01 O 12 F 1.03 was investigated in laboratory heating experiments at 1, 10, 100, and 1000 h at temperatures ranging from 40 to 360°C. For each of the approximately 105 heating experiments, annealing was characterized by measuring the lengths of confined tracks in mineral sections oriented parallel to the c axis and the acute angles between azimuths of the tracks and the c axis. Annealing is characterized by the monotonic decrease in etched track length with increasing temperature or heating time. Track shortening is anisotropic at all stages of fading: tracks parallel to c are most resistant to shortening, tracks perpendicular to c are at least resistant to shortening, and tracks at intermediate angles have intermediate annealing resistances. The relationship between mean track length and track length parallel or perpendicular to c is approximately linear. The decrease in normalized mean track length ( r ) with increasing temperature ( T ) or heating time ( t ) for the fluorapatite and Sr fluorapatite data presented here, as well as the annealing data of et al. (1986) from Durango apatite, is best described by the equation g ( r ; , ) = C 0 + [ C 1 ln t + C 2 ]/[(1/ T ) - C 3 ], where g ( r ; , ) is a power transform of r, and , , C 0 , C 1 , C 2 , and C 3 are parameters. On the Arrhenius diagram, the fading contours (contours of constant r ) for this model equation plot as a series of straight lines that intersect at a single point termed the "crossover point." For the fluorapatite and Sr-fluorapatite data presented here, the crossover points occur within the interval 523° C T 957° C , 10 -5 t 10 -2 s . This point is interpreted to represent the limit of stability of tracks in apatite. Activation energies, which are proportional to the slopes of the fading contours, increase from about 20 kcal /mol at the onset of annealing to about 66 kcal /mol at the final stages of fading. This increase indicates that tracks become more resistant to shortening with progressive annealing. The crossover points and activation energies for the fluorapatite and Sr-fluorapatite model equations are not significantly different at the 5% level. We conclude that, to the first order, the annealing resistance of these two samples as characterized by normalized mean length of etched tracks is identical. The model equations developed from these data sets probably provide reasonable first-order predictions of track annealing at geological time scales. In particular, they predict between about 10 and 15% shortening at ambient temperatures over time scales of 1 my to 1 by, which is consistent with the observation that spontaneous tracks in apatite are between 10 and 20% shorter than induced tracks. However, additional testing is required before these models can be used to interpret measured length distributions on a routine basis.
Cameron Maryellen
Crowley Kevin D.
Schaefer L. R.
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