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Step annealing in radiation damage in solids
Notes
2449
In these reactions N'-methylguanylurea is a typical representative of a series of substituted alkylguanylureas, which are now being studied. The structures of many of the complexes are being elucidated by resolution into optically active antipodes.
Acknowledgement--It is a pleasure to express our gratitude to the Council of Scientific and Industrial Research, Delhi, for financial support. We wish to record also our heartfelt thanks to Prof. SANTZ RANJAN PAUX for his interest in our project. Inorganic Chemistry Laboratory The University of Burdwan Burdwan, West Bengal India
R. L. DUT3A A. SYAMAL
J. Inorg. Nucl. Chem. 1965, Vol. 27, pp. 2449 to 2450. Pergamon Press Ltd. Printed in Northern Ireland
Step annealing in radiation damage in solids (Received 18 Janualy 1965) IN THEIR study of the kinetics of two stage annealing of irradiation induced damage in various solids (trisacetylacetone Co(III) and phosphates)/x,~ AMARNATH et al. and MADDOCKet al. respectively observed that if the solid is first annealed at a temperature T1 for a time tl, and subsequently at temperature T2 (T2 > T0 for a time t~, then the measured value of a property (e.g., percent separable activity in (n, 7) reaction) is greater than if the solid is directly heated at temperature 7"2 for time t~ ÷ t~ (i.e. in a single stage). AMARNATH et al? explained these results on the basis of competitive reactions, which remove the metastable species from the annealing sites or incapacitate it from annealing. Following the mathematical formulation of the problem by PRIMAK,131 the present author finds that this difference between a single stage and double stage annealing is to be expected irrespective of the mechanism of annealing. Let us consider for first order reactions the first of the two successive stages of step annealing. If tt is the time sufficiently long to advance the characteristic annealing function at least several times nrl (~'~ -- k6, k being the Boltzmann constant), for which the first stage of step annealing has been conducted at temperature T~, the property will change, and at this stage the spectrum of activation energy could be written as p~ = p0 (e) exp ( - A t l e
~/7,)
!1)
where p0 is the distribution function of e and has the units [(units of property)/eV] and A is the frequency factor. If at this point, second stage annealing is started at T.d and continued for time t2 the property P~, at the end of the double stage annealing will be given by
PD
==
p0 (e) exp ( Aqe E/'rl) exp ( - At2e ~/72)de.
I1, AMAR NATH, K. S. VENKATESWARLUand J. SHANKAR, Proc. Indian Acad. Sci. 46, 30 (1957). ~*' R. F. C. CLARI~SE and A. G. MADDOCK, Trans Farad. Soc. 59, 935 (1963). Is, W. PRIMAK, Phys. Rev. 100, 1677 (1955).
2450
Notes
The property Ps, o f both stages were at T2 for time (tx ÷ t~) i.e., in single stage annealing, will then be p0 (e) exp (-At~e-~h-~) exp (--At~e-~/~-2) de.
Ps =
(3)
The factors o f the integrands (2) and (3) are positive and differ in second factor only. Since "r2 >
"r 1
exp (--At~e-~/'ra) > exp (--A6e-~/~-2)
.'.
PD>Ps.
The same can be seen to be true for all orders o f reactions. Giving the same argument as above, for n # l, Equations (2) and (3) could be written as
j
t~ oo
P, =
p0 ( e ) [ 1 - (1 -- n)Btle-~/T1]l/1-~[1- (1 -- n)Bt~e-8/.rz]1/1-~ de
(4)
0
and
Ps =
fo
p0 ( e ) [ 1 - ( 1 - n)Btle-8/T2ll/1-n[1 -- ( 1 - n)Bt~e-8/-r2]t/l-" de.
(5)
The factors o f the integrands (4) and (5) are positive and differ only in second factor. Again, since T2 >
T1
Btle-~/.2 > Btle-~/rl when n < 1, (1 -- n) is ( + v e ) , so --(1 -- n)B6e-e/'r2 < --(1 -- n)Btte-~/-rt and
.'. [1 -- (1 -- n)B6e ~/~-di n - " < [1 -- (1 -- n)B6e-8/¢dl/I-"
Thus it is seen that P~) > Ps. Similarly when n > 1, (1 - n) is ( - v e ) , so --(1 -- n)Bt~e-E/T~ > --(1 -- n)B6e-~/.q or [1 -- (1 -- n)Btae-~/.72]~p-n < [1 -- (1 -- n)Btxe-*/r~] 1/1-" from which follows that P9 > Ps. Thus the measured value o f a property at any time will always be higher (qualitatively speaking) in double stage annealing at the higher temperature. In the case o f the data on cobalt acetylacetonate, AMAR NATH et al. ~ have found that the property reaches a saturation value with time at any given temperature and that retention (100-percent separable activity) never reaches 100 per cent. However, caution must be exercised in interpreting the kinetic data since the above mathematical analysis shows at least qualitatively the property is expected to be higher in a double stage c o m p a r e d to a single stage annealing at the higher temperature.
Acknowledgement--The author is indebted to Drs. J. SHANKER.and P. G. KHUBCHANDANI for helpful discussions.
Chemistry Division Atomic Energy Establishment Trombay Bombay 28.
M. LAL
2449
In these reactions N'-methylguanylurea is a typical representative of a series of substituted alkylguanylureas, which are now being studied. The structures of many of the complexes are being elucidated by resolution into optically active antipodes.
Acknowledgement--It is a pleasure to express our gratitude to the Council of Scientific and Industrial Research, Delhi, for financial support. We wish to record also our heartfelt thanks to Prof. SANTZ RANJAN PAUX for his interest in our project. Inorganic Chemistry Laboratory The University of Burdwan Burdwan, West Bengal India
R. L. DUT3A A. SYAMAL
J. Inorg. Nucl. Chem. 1965, Vol. 27, pp. 2449 to 2450. Pergamon Press Ltd. Printed in Northern Ireland
Step annealing in radiation damage in solids (Received 18 Janualy 1965) IN THEIR study of the kinetics of two stage annealing of irradiation induced damage in various solids (trisacetylacetone Co(III) and phosphates)/x,~ AMARNATH et al. and MADDOCKet al. respectively observed that if the solid is first annealed at a temperature T1 for a time tl, and subsequently at temperature T2 (T2 > T0 for a time t~, then the measured value of a property (e.g., percent separable activity in (n, 7) reaction) is greater than if the solid is directly heated at temperature 7"2 for time t~ ÷ t~ (i.e. in a single stage). AMARNATH et al? explained these results on the basis of competitive reactions, which remove the metastable species from the annealing sites or incapacitate it from annealing. Following the mathematical formulation of the problem by PRIMAK,131 the present author finds that this difference between a single stage and double stage annealing is to be expected irrespective of the mechanism of annealing. Let us consider for first order reactions the first of the two successive stages of step annealing. If tt is the time sufficiently long to advance the characteristic annealing function at least several times nrl (~'~ -- k6, k being the Boltzmann constant), for which the first stage of step annealing has been conducted at temperature T~, the property will change, and at this stage the spectrum of activation energy could be written as p~ = p0 (e) exp ( - A t l e
~/7,)
!1)
where p0 is the distribution function of e and has the units [(units of property)/eV] and A is the frequency factor. If at this point, second stage annealing is started at T.d and continued for time t2 the property P~, at the end of the double stage annealing will be given by
PD
==
p0 (e) exp ( Aqe E/'rl) exp ( - At2e ~/72)de.
I1, AMAR NATH, K. S. VENKATESWARLUand J. SHANKAR, Proc. Indian Acad. Sci. 46, 30 (1957). ~*' R. F. C. CLARI~SE and A. G. MADDOCK, Trans Farad. Soc. 59, 935 (1963). Is, W. PRIMAK, Phys. Rev. 100, 1677 (1955).
2450
Notes
The property Ps, o f both stages were at T2 for time (tx ÷ t~) i.e., in single stage annealing, will then be p0 (e) exp (-At~e-~h-~) exp (--At~e-~/~-2) de.
Ps =
(3)
The factors o f the integrands (2) and (3) are positive and differ in second factor only. Since "r2 >
"r 1
exp (--At~e-~/'ra) > exp (--A6e-~/~-2)
.'.
PD>Ps.
The same can be seen to be true for all orders o f reactions. Giving the same argument as above, for n # l, Equations (2) and (3) could be written as
j
t~ oo
P, =
p0 ( e ) [ 1 - (1 -- n)Btle-~/T1]l/1-~[1- (1 -- n)Bt~e-8/.rz]1/1-~ de
(4)
0
and
Ps =
fo
p0 ( e ) [ 1 - ( 1 - n)Btle-8/T2ll/1-n[1 -- ( 1 - n)Bt~e-8/-r2]t/l-" de.
(5)
The factors o f the integrands (4) and (5) are positive and differ only in second factor. Again, since T2 >
T1
Btle-~/.2 > Btle-~/rl when n < 1, (1 -- n) is ( + v e ) , so --(1 -- n)B6e-e/'r2 < --(1 -- n)Btte-~/-rt and
.'. [1 -- (1 -- n)B6e ~/~-di n - " < [1 -- (1 -- n)B6e-8/¢dl/I-"
Thus it is seen that P~) > Ps. Similarly when n > 1, (1 - n) is ( - v e ) , so --(1 -- n)Bt~e-E/T~ > --(1 -- n)B6e-~/.q or [1 -- (1 -- n)Btae-~/.72]~p-n < [1 -- (1 -- n)Btxe-*/r~] 1/1-" from which follows that P9 > Ps. Thus the measured value o f a property at any time will always be higher (qualitatively speaking) in double stage annealing at the higher temperature. In the case o f the data on cobalt acetylacetonate, AMAR NATH et al. ~ have found that the property reaches a saturation value with time at any given temperature and that retention (100-percent separable activity) never reaches 100 per cent. However, caution must be exercised in interpreting the kinetic data since the above mathematical analysis shows at least qualitatively the property is expected to be higher in a double stage c o m p a r e d to a single stage annealing at the higher temperature.
Acknowledgement--The author is indebted to Drs. J. SHANKER.and P. G. KHUBCHANDANI for helpful discussions.
Chemistry Division Atomic Energy Establishment Trombay Bombay 28.
M. LAL