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Fission track closure temperatures
Nuclear Tracks, Vol. 12, Nos I-6, pp. 921-925, Int. J. Radiat. Appl. Instrum., Part D Printed in Great Britain.
1986.
0191-278X/86 $3.00+.00 Pergamon Journals Ltd.
FISSION TRA(X CLOSURE
K. J ~ s
and S.A. Durrani
D e p a r t m e n t of Physics, Oniversity of Birmingham, Birminghmm B15 2TT, U.K.
ABSTRACT
A numerical method is described for the calculation of fission track closure temperatures, which is based on the empirical equations of Bertagnolli e t a l . (1983). Unlike the method of ~ (1977), the increase in activation energy during annealing is taken into account. Closure temperatures of several terrestrial minerals have been calculated from published experimental annealing data. The results aze consistently 7 to 16 "C higher than those obtalned with the same data when Raack's method is used. In meteoritic minerals, the prims~mtl track-fozming species was pred-m4nantly a44pu, which h~s a mean life (. 118 Myr) ccm%~xable with typical cooling times. Inclusion of an appropriate exponential decrease in the track production rate, to account for the radloactive decay of the parent isotope, has been found to produce only a slight change in the calculated closure temperatures and may be neglacted in most calculations: particularly for cooling rates greater than about 3 eC ~ E -£ . m Annealing; Activation energy; Fission track age; Closure temperature; Track growth curve; Cooling rate; Meteorite parent bodies; Plutoniu~-244; Track fading; IsotherE~l intervals. INTRODO~TION It is well known that ages obtained by the fission track method do not necessarily date the true solidification age of either terrestrial or meteoritic minerals, but are, in fact, dependent upon the thszwal history of the sample. Fission track dates are closely associated with the so-called closure temperature of the system, which represents the critical temperature in the cooling history of the mineral, at which track retention effectively sets in. The fission track age, as with other radiometric ages (such as Rb-SE or K-At ages), defines the time at which the system cooled to its closure temperature; but because of the relatively high sensitivity of fission tracks to fading at elevated te|~eratures, compared with the loss of radiogenic Sr or Ar by diffusion, the fission track closure temperatures (~aa~k, 1977; Saini, 1979; Nagpaul, 1982) are considerably lower than those of the other radiometric systems (Dodson, i~79). This offers the possibility of dating any later low-tem%oerature episodes in the cooling histories of both rock and meteoritic samples. Moreover, since different types of minerals have different closure temperatures, i t is poasible to date the times at which the rock sample cooled past the closure temperature of each of its constituent minerals. So, knowing the individual fission track closure temperatures (and in some cases also the R~-Sr or K-At closure temperatures ), the cooling history of the sam%~le can he recomstructed. This haJ obvious geological applications: for the dMrtermiuation of uplift rates for ~ D l e . In the study of meteorites, cooling rates inferred in this way enable estimates of the sizes of meteorite parent bodies to he made. To accomplish the above objectives requires an accurate knowledge of the fission track closure temperatures of a wide range of mineral types. ~ae closure temperature also varies with the actual cooling rate of the mineral. For slow cooling, the mineral spends a greater
921
922
K. JAMES AND S. A. DURRANI
time overall at elevated temperatures and so a given d e g r e e of track fading may be brought about at a lower temperature than for fast cooling. So the closure temperature increases with increasing cooling rate. Accordingly, in the present study, the fission track closure temperatures of several terrestrial LineralB have been calculated, from p~blished isothermal annea1~ng data, for a range of cooling rates between . 0.i and I00 oC Myr-'. CALCULATION OF CLOSURE TERK~ERATURES In order to calculate the fission track closure temperature of a mineral, the track growth curve, which represents the build-up of the fission track density during cooling, must first be obtained. As the mineral cools through the temperature zone of partial track stability, the fission track density increases, gradually at first and then more rapidly as the temperature approaches t h e b o u n d a r y between the zones of partial and total trac~ stability. Finally, when the temperature has reached the zone of total stability, the ~ l a t i o n of tracks is governed solely by the fission track production rate. When obtaining a fission track age, one assumes that the tracks suddenly become stable at the time (which m a y be termed the "closure time") corresponding to the age, and that no fading has occurred since: the apparent fission track age is then obtained by effectively extrapolating the track growth CtLrve back to the time axis from the zone of total track stability. The clostLre temperature is definnd as the temperature of the mineral at t h e time given b y i t s apparent f i s s i o n t r a c k age; so t h a t i f t h e t r a c k growth curve and c l o s u r e time can be d e t e ~ n e d , t h e c l o s u r e temperature may be found from t h e p a r t i c u l a r time-dependent temperature f u n c t i o n T(t), assumed for the cooling. A numerical method for the calculation of track growth curves, based upon a differential equation describing the production and fading of fission tracks in a slowly cooling mineral, has been described b y - ~ k (1977). In this method, the steady cooling is a ~ , v - ~ m t e d to a large n~mber of stepwise decrements in tem@erature, s e p a r a t e d b y short isothermal intervals, and the fading of both newly formed and old partially annealed tra~ul is calculated during each interval. However, in saA~k's method the fading of old tracks is calculated fz~m extrapolated Arrhenius plot data obtained for unannealed fission tracks, and so the increase in annealing activation energy that would be expected for these o l d t r a c k s (Fleischer et al., 1975) is not taken into account. This results in calculated cloBure temperatures which are lower than would otherwise be obtained. In order to allow for the variation of activation energy with the degree of annealing, a different numerical method for track growth curve calculations has been used. This is based upon the empirical annealing equation: dA ] = - da°(A)'A" t
exp [- kT(t) E(A~
(1)
given by B e ~ l l i et al. (1983), which describes the thermal annealing of a single fission track under a time-dependant temperature, T(t). The dependent variable A in the above equation is defined by Bertagnolli et al. as the ratio of the lengths of thermally-shortened to full-length (unannealed) fission tracks (A is a fu~-tion of both T(t ) and the time (T) of production of the track); a(A) is an annealing coefficient(with units s-~); E(A) is the activation energy for annealing, and k is the B o l t ~ a m m constant. This can he rewritten as
d~ = _ dt
where
exp
(~) -
(2) kT( t
q(~) = tn (ao(~).~)
(3)
and, as indicated by Berta~jnolli et al. (1983), the functions E(A) and reasonable degree of accuracy, be a~Drn~4emted to s~cond-order p o l ~ : E(A) = e o + e£A +
q(a)
can,
to
ezAz (4)
q(A) -- qo + q~A + qzA z For the purposes of calculating the track growth curve,
it is convenient to ap~zowlmate
the
a
FISSION TRACK CLOSURE TEMPERATURES
923
steady production of tracks to many discrete production events: each one producing a group of tracks which are subseqently partially or totally annealed during the remainder of the cooling period. In this case, it is more useful to take A as the surviving fraction, at some time (t), of any particular group of tracks produced at an earlier time (T), rather than the reduced relative track length as used by Bertagnolli et al. (1983), and to assumm that equation (i) then adequately describes the fading of track density during annealing. In order to use equations (2) and (4) to calculate relationshipe between track density and fission track age, Bertagnolli et al. assume a direct proportionality between the reduction in the relative track length and in the relative track density. The a s s ~ i o n that equation (1) can he used to describe the reduction in density of a single group of tracks is no greater an a~prow~-~tion than the one used by the above authors. In fact, if the data used are based on track density measurements, then the fitted parameters of equation (4) and the resulting calculations will reflect more accurately the changes in track density during cooling. E(A) and q(A) can he determined from ezperimental data obtained from measurements of the reduced track density resulting from isothermal annealing of freshly induced fission tracks in each mineral of interest, and the coefficients of the polynomials in Eq. (4) are then found from a simple second-order polynomial fit to the values of E( A ) and q( A ). The steady rate of production of fission surface, at a time t = 7, is given by
~T) = c s~ where
C is
[-
a constant
tracks,
per
unit
area
of
an
internal
~..T ] depending
crystal-
(s) on the
mean etchable
range
of
the
fission
concentration and spontaneous fission decay constant of the track-forming the total radioactive decay constant of the track forming species. The growth of the fission track surface-density t P(t) = C Io e,~ [- AR.T ] A(t,T) aT
tracks
species~
and on the
and kR is
P(t), with time, is then given by (6)
By dividing the continuous time-dependent fall in temperature T(t), during cooling, into many small isothermal intervals of duration ~t, Eq. (2) can he al>pliad to each group of tracks pr(x]uced at a variable time T to calculate the reduction (~A) in A during successive temperature intervals, and so to obtain tabulated values of A(t,T) for a given temperature function T(t). These values are then used in a similar stepwise calculation to determine the time-dependent surface track density P( t ) b y aRvrow~ ~-~ting the integral in Eq. (6) to a s,~tion of the contributions of many discrete production events to the total fission track surface-density at time t. DISCUSSION OF RESULTS A N D CONCLUSIONS Using the method described in the preceding section, the closure temperatures of several terrestrial minerals have been calculated from published isothermal annealing data. These are shown in Fig. 1 for a range of appropriate cooling rates, using a38u as the track producing isotope (with A R = 1.551 x l 0 -4 Myr-i). Since the annealing "sensitivity" of fission tracks in a given mineral depends on the subsequent etching conditions employed, these etching conditions are specified for each mineral in table I, together with the source of data used in the calculations. For co~oexison, calculations have also been performed, with the same data, using ~_~ck°s method (Haack, 1977), which yield closure temperatures that are typically 7 to 16 oC lower than those calculated by the method described above. This difference is to be expected, as Haack's method neglects the increase in activation energy which occurs as the annealing progresses (Fleischer et al., 1975). In both cases, the calculated closure temml~ratures increase with increasing cooling rate: typically, a 12 to 20 oC increase occurs for a change of one order of magnitude in the co(ling rate. In the case of very ancient meteoritic minerals (over . 4 Glrr old), the dominant trackforming species is usually Z44Pu, which has a mean life (. I18 Mlrr) comparable with typical times taken by many meteorite parent bodies to cool through the partial track-stability zone. Inclusion of such a rapid decay of the track-forming species in the calculations may intuitively be expected to have a Considerable effect on the resulting values of closure
924
K. JAMES and S. A. DURRANI
350
.
.
~ . . . . ~ . ~
~ ~ ~
0.1
.
.
6(b,) I'0 ~OLI~
Fig. i.
,
,
I0"0
100.0
L~.~m C C / N y r )
Calculated closure temperatures as a function of the assumed linear cooling rate for several terrestrial minerals. The solid lines (a) represent results of calculations performad b y the method described in this paper. Broken lines (b) are the results obtained by ~2tck's method using the same data. The serial ntmbers on the curves are those listed in table i.
130
11o
'~ 1oo
/.
t
7O
60
50
I 0.1
I 1-0
1 10.0
I 100.0
o:)ot.I~X~ ~.I"S ( ' c / l , l y z )
Fig.
2.
Calculated closure t~ratures o f ~ 4 ~ a t i t e b a s e d o n t h e d a t a o f W a t t ( 1 9 8 4 ) . The :mild line z e p r e s e n t m o a l c ~ l a t l o r ~ p e r f o z m e d u s i n g d e c a y i n g z3aU a s t h e t ~ forming i s o t o p e , t h e r e s u l t s o f ~biob axe i ~ n t i ~ t o those obtained a s s u m i n g no decay. The b r o k e n l i n e x e p = e s e n t s c l o s u r e t e m p e r a t u r e s c a l c u l a t e d u s i n g z 4 , ~ as
t h e t r a c k forming s p e c i e s .
FISSION TRACK CLOSURE TEMPERATURES
925
temperature. As shown in Fig. 2, the calculated closure temperatures have, however, been found to i n c r e u e by only a few oC for cooling rates comparable with those of slowly cooling chondritic meteorite parent bodies (. 1 oC Myr -i ). For faster cooling (greater than about 3 °C Myr -~ ), the calculated closure temperatures coincide with those values calculated assuming no decay of the parent nuclide. Even in the case of slow cooling, such a change is not likely to be very significant in the context of probable experimental errors involved. We therefore conclude that the us%umption of a constant concentration of the track forming nuclide ~ay be used in most calculations of closure temperatures without incurring any significant errors. Table 1
Details of the curves shown in Fig. I, with the source of experimental data and etching conditions specified for each mineral
CURVE
MINERAL
ETCHING CONDITIONS
S O U R C E O F DATA
1 a,b
Sphene
HCI, 45 m i n
N a e s e r a n d Faul (1969)
2 a,b
Sphene
H20: conc. HCI: conc. H N O 3 :48~ H F = 6z3:2:1, 30 St room temperature
Watt
3 a,b
Tourmaline
48S HF, 15 - 20 m i n
Lal e_~ a_!l, (1977)
4 a,b
Epidote
209 NaOH= 5ml HgO , various timeg, boilin 9
Sainie__~, (1978)
5 a,b
Apatite
IM HNOa, 60 s, room temperature
Watt
6 a,b
Chlori~e
4 8 ~ HF, 3 5 - 4 0
, 90"C
min
, 30°C
, 60"C
(1984)
(1984)
S h a r m a e~ al. (1977)
R(m~E~LEDG~m~ K.J. gratefully acknowledges Engineering Research Council.
receipt
of
financial
support
from
the
U.K.
Science
and
RE~m~CES Bertagnolli E., Kiel R. and Pahl M. (1983) Thermal history and length distribution of fission tracks in apatite: Part I. Nucl. T r a c ~ 7, 163-177. Dodson M°R. (1979) Theory of cooling ages. In: Lectures in IsotoDe Geoloqy. (Jager E. and Hunziker J.C., eds. ) p p 194-202, Springer-Verlag, Berlin. Fleischer R.L., Price P.B. and Walker R.M. (1975) Nuclear tracks in s o l i ~ . University of California Press, Berkeley. ~aack U. ( 1977 ) The closing temperature for fission track retention in minerals. Am. J. ~ci. 277, 459--464. Lal N., Parshad R. and NagLm/al K.K. (1977) Fission track etching and annealing of tourmaline. Nucl. Track Det. i, 145--148. Naeser C.W. and Faul H. (1969) Fission track annealing in apatite and sphene. J. Geophvs. Re~, 74, 705-710. Nagpaul K.K. (1982) Fission track geochronology of India. In: ~ (Goswami J.N., e4. ) p p 53-65, Indian Academy of Sciences. Sa/ni H. S., Sharma O.P. and Nagpaul K.K. ( 1979 ) Fission fragment range and closing temperature for track retention in minerals. Nucl. Track~ 3, 139-141. Saini S.S, Sharma O.P., Parshad R. and Nagpaul K.K. ( 1978 ) Fission track annealing characteristics of epidote: applications to geochronology and geology. Nucl. Track Det. ~, 133-140. Shaxma O.P, Bal K.D. and Nagpaul K.K. (1977) Fission track annealing and age determination of chlorite. Nucl. Track De~, I, 207-211. Watt S. (1984) The zeta calibrat~Qn of fission track datinu and the thezlmal stability of fission tracks in o e o l o a i ~ material,. Ph.D. Thesis, Dept. of Physics, University of Birmingham.
1986.
0191-278X/86 $3.00+.00 Pergamon Journals Ltd.
FISSION TRA(X CLOSURE
K. J ~ s
and S.A. Durrani
D e p a r t m e n t of Physics, Oniversity of Birmingham, Birminghmm B15 2TT, U.K.
ABSTRACT
A numerical method is described for the calculation of fission track closure temperatures, which is based on the empirical equations of Bertagnolli e t a l . (1983). Unlike the method of ~ (1977), the increase in activation energy during annealing is taken into account. Closure temperatures of several terrestrial minerals have been calculated from published experimental annealing data. The results aze consistently 7 to 16 "C higher than those obtalned with the same data when Raack's method is used. In meteoritic minerals, the prims~mtl track-fozming species was pred-m4nantly a44pu, which h~s a mean life (. 118 Myr) ccm%~xable with typical cooling times. Inclusion of an appropriate exponential decrease in the track production rate, to account for the radloactive decay of the parent isotope, has been found to produce only a slight change in the calculated closure temperatures and may be neglacted in most calculations: particularly for cooling rates greater than about 3 eC ~ E -£ . m Annealing; Activation energy; Fission track age; Closure temperature; Track growth curve; Cooling rate; Meteorite parent bodies; Plutoniu~-244; Track fading; IsotherE~l intervals. INTRODO~TION It is well known that ages obtained by the fission track method do not necessarily date the true solidification age of either terrestrial or meteoritic minerals, but are, in fact, dependent upon the thszwal history of the sample. Fission track dates are closely associated with the so-called closure temperature of the system, which represents the critical temperature in the cooling history of the mineral, at which track retention effectively sets in. The fission track age, as with other radiometric ages (such as Rb-SE or K-At ages), defines the time at which the system cooled to its closure temperature; but because of the relatively high sensitivity of fission tracks to fading at elevated te|~eratures, compared with the loss of radiogenic Sr or Ar by diffusion, the fission track closure temperatures (~aa~k, 1977; Saini, 1979; Nagpaul, 1982) are considerably lower than those of the other radiometric systems (Dodson, i~79). This offers the possibility of dating any later low-tem%oerature episodes in the cooling histories of both rock and meteoritic samples. Moreover, since different types of minerals have different closure temperatures, i t is poasible to date the times at which the rock sample cooled past the closure temperature of each of its constituent minerals. So, knowing the individual fission track closure temperatures (and in some cases also the R~-Sr or K-At closure temperatures ), the cooling history of the sam%~le can he recomstructed. This haJ obvious geological applications: for the dMrtermiuation of uplift rates for ~ D l e . In the study of meteorites, cooling rates inferred in this way enable estimates of the sizes of meteorite parent bodies to he made. To accomplish the above objectives requires an accurate knowledge of the fission track closure temperatures of a wide range of mineral types. ~ae closure temperature also varies with the actual cooling rate of the mineral. For slow cooling, the mineral spends a greater
921
922
K. JAMES AND S. A. DURRANI
time overall at elevated temperatures and so a given d e g r e e of track fading may be brought about at a lower temperature than for fast cooling. So the closure temperature increases with increasing cooling rate. Accordingly, in the present study, the fission track closure temperatures of several terrestrial LineralB have been calculated, from p~blished isothermal annea1~ng data, for a range of cooling rates between . 0.i and I00 oC Myr-'. CALCULATION OF CLOSURE TERK~ERATURES In order to calculate the fission track closure temperature of a mineral, the track growth curve, which represents the build-up of the fission track density during cooling, must first be obtained. As the mineral cools through the temperature zone of partial track stability, the fission track density increases, gradually at first and then more rapidly as the temperature approaches t h e b o u n d a r y between the zones of partial and total trac~ stability. Finally, when the temperature has reached the zone of total stability, the ~ l a t i o n of tracks is governed solely by the fission track production rate. When obtaining a fission track age, one assumes that the tracks suddenly become stable at the time (which m a y be termed the "closure time") corresponding to the age, and that no fading has occurred since: the apparent fission track age is then obtained by effectively extrapolating the track growth CtLrve back to the time axis from the zone of total track stability. The clostLre temperature is definnd as the temperature of the mineral at t h e time given b y i t s apparent f i s s i o n t r a c k age; so t h a t i f t h e t r a c k growth curve and c l o s u r e time can be d e t e ~ n e d , t h e c l o s u r e temperature may be found from t h e p a r t i c u l a r time-dependent temperature f u n c t i o n T(t), assumed for the cooling. A numerical method for the calculation of track growth curves, based upon a differential equation describing the production and fading of fission tracks in a slowly cooling mineral, has been described b y - ~ k (1977). In this method, the steady cooling is a ~ , v - ~ m t e d to a large n~mber of stepwise decrements in tem@erature, s e p a r a t e d b y short isothermal intervals, and the fading of both newly formed and old partially annealed tra~ul is calculated during each interval. However, in saA~k's method the fading of old tracks is calculated fz~m extrapolated Arrhenius plot data obtained for unannealed fission tracks, and so the increase in annealing activation energy that would be expected for these o l d t r a c k s (Fleischer et al., 1975) is not taken into account. This results in calculated cloBure temperatures which are lower than would otherwise be obtained. In order to allow for the variation of activation energy with the degree of annealing, a different numerical method for track growth curve calculations has been used. This is based upon the empirical annealing equation: dA ] = - da°(A)'A" t
exp [- kT(t) E(A~
(1)
given by B e ~ l l i et al. (1983), which describes the thermal annealing of a single fission track under a time-dependant temperature, T(t). The dependent variable A in the above equation is defined by Bertagnolli et al. as the ratio of the lengths of thermally-shortened to full-length (unannealed) fission tracks (A is a fu~-tion of both T(t ) and the time (T) of production of the track); a(A) is an annealing coefficient(with units s-~); E(A) is the activation energy for annealing, and k is the B o l t ~ a m m constant. This can he rewritten as
d~ = _ dt
where
exp
(~) -
(2) kT( t
q(~) = tn (ao(~).~)
(3)
and, as indicated by Berta~jnolli et al. (1983), the functions E(A) and reasonable degree of accuracy, be a~Drn~4emted to s~cond-order p o l ~ : E(A) = e o + e£A +
q(a)
can,
to
ezAz (4)
q(A) -- qo + q~A + qzA z For the purposes of calculating the track growth curve,
it is convenient to ap~zowlmate
the
a
FISSION TRACK CLOSURE TEMPERATURES
923
steady production of tracks to many discrete production events: each one producing a group of tracks which are subseqently partially or totally annealed during the remainder of the cooling period. In this case, it is more useful to take A as the surviving fraction, at some time (t), of any particular group of tracks produced at an earlier time (T), rather than the reduced relative track length as used by Bertagnolli et al. (1983), and to assumm that equation (i) then adequately describes the fading of track density during annealing. In order to use equations (2) and (4) to calculate relationshipe between track density and fission track age, Bertagnolli et al. assume a direct proportionality between the reduction in the relative track length and in the relative track density. The a s s ~ i o n that equation (1) can he used to describe the reduction in density of a single group of tracks is no greater an a~prow~-~tion than the one used by the above authors. In fact, if the data used are based on track density measurements, then the fitted parameters of equation (4) and the resulting calculations will reflect more accurately the changes in track density during cooling. E(A) and q(A) can he determined from ezperimental data obtained from measurements of the reduced track density resulting from isothermal annealing of freshly induced fission tracks in each mineral of interest, and the coefficients of the polynomials in Eq. (4) are then found from a simple second-order polynomial fit to the values of E( A ) and q( A ). The steady rate of production of fission surface, at a time t = 7, is given by
~T) = c s~ where
C is
[-
a constant
tracks,
per
unit
area
of
an
internal
~..T ] depending
crystal-
(s) on the
mean etchable
range
of
the
fission
concentration and spontaneous fission decay constant of the track-forming the total radioactive decay constant of the track forming species. The growth of the fission track surface-density t P(t) = C Io e,~ [- AR.T ] A(t,T) aT
tracks
species~
and on the
and kR is
P(t), with time, is then given by (6)
By dividing the continuous time-dependent fall in temperature T(t), during cooling, into many small isothermal intervals of duration ~t, Eq. (2) can he al>pliad to each group of tracks pr(x]uced at a variable time T to calculate the reduction (~A) in A during successive temperature intervals, and so to obtain tabulated values of A(t,T) for a given temperature function T(t). These values are then used in a similar stepwise calculation to determine the time-dependent surface track density P( t ) b y aRvrow~ ~-~ting the integral in Eq. (6) to a s,~tion of the contributions of many discrete production events to the total fission track surface-density at time t. DISCUSSION OF RESULTS A N D CONCLUSIONS Using the method described in the preceding section, the closure temperatures of several terrestrial minerals have been calculated from published isothermal annealing data. These are shown in Fig. 1 for a range of appropriate cooling rates, using a38u as the track producing isotope (with A R = 1.551 x l 0 -4 Myr-i). Since the annealing "sensitivity" of fission tracks in a given mineral depends on the subsequent etching conditions employed, these etching conditions are specified for each mineral in table I, together with the source of data used in the calculations. For co~oexison, calculations have also been performed, with the same data, using ~_~ck°s method (Haack, 1977), which yield closure temperatures that are typically 7 to 16 oC lower than those calculated by the method described above. This difference is to be expected, as Haack's method neglects the increase in activation energy which occurs as the annealing progresses (Fleischer et al., 1975). In both cases, the calculated closure temml~ratures increase with increasing cooling rate: typically, a 12 to 20 oC increase occurs for a change of one order of magnitude in the co(ling rate. In the case of very ancient meteoritic minerals (over . 4 Glrr old), the dominant trackforming species is usually Z44Pu, which has a mean life (. I18 Mlrr) comparable with typical times taken by many meteorite parent bodies to cool through the partial track-stability zone. Inclusion of such a rapid decay of the track-forming species in the calculations may intuitively be expected to have a Considerable effect on the resulting values of closure
924
K. JAMES and S. A. DURRANI
350
.
.
~ . . . . ~ . ~
~ ~ ~
0.1
.
.
6(b,) I'0 ~OLI~
Fig. i.
,
,
I0"0
100.0
L~.~m C C / N y r )
Calculated closure temperatures as a function of the assumed linear cooling rate for several terrestrial minerals. The solid lines (a) represent results of calculations performad b y the method described in this paper. Broken lines (b) are the results obtained by ~2tck's method using the same data. The serial ntmbers on the curves are those listed in table i.
130
11o
'~ 1oo
/.
t
7O
60
50
I 0.1
I 1-0
1 10.0
I 100.0
o:)ot.I~X~ ~.I"S ( ' c / l , l y z )
Fig.
2.
Calculated closure t~ratures o f ~ 4 ~ a t i t e b a s e d o n t h e d a t a o f W a t t ( 1 9 8 4 ) . The :mild line z e p r e s e n t m o a l c ~ l a t l o r ~ p e r f o z m e d u s i n g d e c a y i n g z3aU a s t h e t ~ forming i s o t o p e , t h e r e s u l t s o f ~biob axe i ~ n t i ~ t o those obtained a s s u m i n g no decay. The b r o k e n l i n e x e p = e s e n t s c l o s u r e t e m p e r a t u r e s c a l c u l a t e d u s i n g z 4 , ~ as
t h e t r a c k forming s p e c i e s .
FISSION TRACK CLOSURE TEMPERATURES
925
temperature. As shown in Fig. 2, the calculated closure temperatures have, however, been found to i n c r e u e by only a few oC for cooling rates comparable with those of slowly cooling chondritic meteorite parent bodies (. 1 oC Myr -i ). For faster cooling (greater than about 3 °C Myr -~ ), the calculated closure temperatures coincide with those values calculated assuming no decay of the parent nuclide. Even in the case of slow cooling, such a change is not likely to be very significant in the context of probable experimental errors involved. We therefore conclude that the us%umption of a constant concentration of the track forming nuclide ~ay be used in most calculations of closure temperatures without incurring any significant errors. Table 1
Details of the curves shown in Fig. I, with the source of experimental data and etching conditions specified for each mineral
CURVE
MINERAL
ETCHING CONDITIONS
S O U R C E O F DATA
1 a,b
Sphene
HCI, 45 m i n
N a e s e r a n d Faul (1969)
2 a,b
Sphene
H20: conc. HCI: conc. H N O 3 :48~ H F = 6z3:2:1, 30 St room temperature
Watt
3 a,b
Tourmaline
48S HF, 15 - 20 m i n
Lal e_~ a_!l, (1977)
4 a,b
Epidote
209 NaOH= 5ml HgO , various timeg, boilin 9
Sainie__~, (1978)
5 a,b
Apatite
IM HNOa, 60 s, room temperature
Watt
6 a,b
Chlori~e
4 8 ~ HF, 3 5 - 4 0
, 90"C
min
, 30°C
, 60"C
(1984)
(1984)
S h a r m a e~ al. (1977)
R(m~E~LEDG~m~ K.J. gratefully acknowledges Engineering Research Council.
receipt
of
financial
support
from
the
U.K.
Science
and
RE~m~CES Bertagnolli E., Kiel R. and Pahl M. (1983) Thermal history and length distribution of fission tracks in apatite: Part I. Nucl. T r a c ~ 7, 163-177. Dodson M°R. (1979) Theory of cooling ages. In: Lectures in IsotoDe Geoloqy. (Jager E. and Hunziker J.C., eds. ) p p 194-202, Springer-Verlag, Berlin. Fleischer R.L., Price P.B. and Walker R.M. (1975) Nuclear tracks in s o l i ~ . University of California Press, Berkeley. ~aack U. ( 1977 ) The closing temperature for fission track retention in minerals. Am. J. ~ci. 277, 459--464. Lal N., Parshad R. and NagLm/al K.K. (1977) Fission track etching and annealing of tourmaline. Nucl. Track Det. i, 145--148. Naeser C.W. and Faul H. (1969) Fission track annealing in apatite and sphene. J. Geophvs. Re~, 74, 705-710. Nagpaul K.K. (1982) Fission track geochronology of India. In: ~ (Goswami J.N., e4. ) p p 53-65, Indian Academy of Sciences. Sa/ni H. S., Sharma O.P. and Nagpaul K.K. ( 1979 ) Fission fragment range and closing temperature for track retention in minerals. Nucl. Track~ 3, 139-141. Saini S.S, Sharma O.P., Parshad R. and Nagpaul K.K. ( 1978 ) Fission track annealing characteristics of epidote: applications to geochronology and geology. Nucl. Track Det. ~, 133-140. Shaxma O.P, Bal K.D. and Nagpaul K.K. (1977) Fission track annealing and age determination of chlorite. Nucl. Track De~, I, 207-211. Watt S. (1984) The zeta calibrat~Qn of fission track datinu and the thezlmal stability of fission tracks in o e o l o a i ~ material,. Ph.D. Thesis, Dept. of Physics, University of Birmingham.