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A new method of dating pottery by thermoluminescence
NUCLEAR
INSTRUMENTS
AND
METHODS
I37
(I976) 565-567;
©
NORTH-HOLLAND
PUBLISHING
CO.
A NEW M E T H O D OF DATING P O T T E R Y BY T H E R M O L U M I N E S C E N C E STEF. C H A R A L A M B O U S
and CHR. MICHAEL
Department of Nuclear Physics, Aristotle University of Thessaloniki, Greece Received 20 April 1976 T h e shape o f the t h e r m o l u m i n e s c e n c e glow-curve o f an archaeological sample depends on its archaeological age. In this work it is d e m o n s t r a t e d that it is possible to obtain in the laboratory a n artificial glow curve identical to the archaeological one. F r o m the conditions o f the laboratory experiment (temperature o f irradiation a n d dose rate), u n d e r which the identity is achieved, it is possible to estimate the archaeological age o f the sample. T h e theory o f the m e t h o d is presented a n d experimental results are given.
1. Introduction
Thermoluminescence is used in a variety of ways for dating geological and archaeological samples. In the present paper, a method of dating ancient pottery is proposed that is based on the study of the shape and properties of the thermoluminescence glow-curve. The physics of the proposed method is as follows: The pottery sample from the time of its baking until the moment of measurement is continually irradiated (a) by its own radioactivity, (b) by the radioactivity of its environment and (c) by cosmic radiation. We call all these radiations archaeological irradiation. The archaeological irradiation is obviously done at the temperature of the archaeological site (at the exact position of the sample). We call this the archaeological temperature. The above processes have two results: a) an increase of the thermoluminescence with dose (.and time) and, b) a decrease of thermoluminescence due to the escape of trapped electrons on account of their thermal motion at the archaeological temperature. The part of the glow-curve affected is that at low temperatures. This is shown explicitly in fig. 1 where the archaeological glow-curve is shown [curve (a)], and also the glow-curve of the sample after a short and intense irradiation at room temperature [curve (A)], which was taken a few hours later. We found that a glow-curve could be taken, with shape identical to that of the archaeological glow-curve, provided the sample was irradiated rapidly with the archaeological dose but at a temperature suitably higher than the archaeological. In cases where a successful coincidence of the archaeological glow-curve with an "equivalent laboratory glow-curve" was possible, the archaeological age of the sample could be found. As is shown below,
the variable parameters that enter into the problem are only the pair: duration and temperature of irradiation in the laboratory.
I
I
~n 4,,
.0 al
e u c o o c
jm~,
E
o /
b
b (3s') ---./ I I I
t'/
100 Temperature
black body" 200 (°C)
Fig. 1. Glow-curves o f the lerissos pottery. C u r v e (a) is the " a r c h a e o l o g i c a l " glow-curve, a n d (A) that o f a recent short a n d intense irradiation at r o o m temperature a n d to the s a m e total dose. Glow-curves similar to the archaeological one can be obtained if the sample is irradiated to the s a m e dose in a short time at a suitably high temperature. Such a curve (a) was obtained at 150 °C in 70 min. Curves (b) a n d (c) resulted f r o m irradiations at 150°C for 35 and 105 min respectively.
566
STEF.
CHARALAMBOUS
2. Theory and experimental results
(1)
where O is the height of the glow-curve at a certain temperature and f ( O ) a function of O that can be considered constant for a wide range of values of O, but different for different points on the glow-curve. The value of fl was found to be constant and the same for all points on the glow-curve. The relation representing decay by second order kinetics is ~) -dNi/dt
= exp(-E/kT) NinPi,
(2)
where Ni is the number of recombination centers (hole traps) which remain vacant and which correspond to the considered point of the glow-curve, and n is the number of trapped electrons. Pi is a probability factor. Comparison of eq. (2) with the experimentally found relation (1), assuming that O is proportional to Ni, gives f l = E / k and f ( O ) = Pin. Under conditions of constant intensity of radiation, the net change of O with time would be given by the relation: dO =aa(O)dt-f(O)
e x p ( - f l / T ) O dr,
(3)
where ~ represents the dose rate. This is the ratio of the total dose 3 divided by the irradiation time t: i.e. ~ = A/t. The function a(6)) is a function of 6) that gives the increase of thermoluminescence per unit dose (without decay). In the case of linear increase of thermoluminescence with dose, a ( O ) is constant. If e x p ( - f l / T ) = c then eq. (3) can be written as: d O = A a(6)) d(ct) - 1"(6)) 6) d(ct).
(4)
ct
The general solution of the differential eq, (4) would be: 0 = eb(A,ct).
(5)
The physical meaning of eq. (5) is that O, on the basis of the above assumption, will be a function of the total dose A and of ct, and independent of the intensity of radiation (dose rate). This means that for the same dose we can have several pairs ca t~, c2t2 . . . . . cit i for wich c I t I = C2t 2 . . . . .
CHR.
MICHAEL
or
For the archaeological pottery from lerissos in Chalkidiki (Greece) that we had at our disposal, it was found experimentally that the decrease of thermoluminescence with time at temperature T, is given by the following relation: dO/dr = - O . J (O) e x p ( - / ] / T ) ,
AND
(6)
t, e x p ( - A E / k T , )
= t~, e x p ( - A E / k T . ) .
(7)
where t ~ is the duration of irradiation in the laboratory and Tt the temperature of irradiation in the laboratory. and for which pairs we have coincidence of the glowcurves. T~, is the "equivalent" temperature of the sample during the time it was buried at the archaeological site. The value of T. is given to a good approximation by the equation: e At:/kT,
=
(e-AE/k~t,
+ e-AE/k'12 + ... + e
'lC/kT"-)/12
,
(8) where T~, T 2 are the mean temperatures of the ground at the depth where the pottery was found, for each of the 12 months of the year. In eq. (7), t~ is the archaeological age. Eq. (7) is the base of the proposed method. The quantities tj and Tj can be measured with great accuracy in the laboratory. A E can be measured by the method proposed by Cameron et al.Z). T~ is estimated from the meteorological data of the region. The measurement technique and analysis of the data will be presented in a more detailed paper. The method described above was applied to pottery samples from lerissos. Typical curves are shown in fig. 1. Curve (a) is the archaeological curve. Curve (b) corresponds to 35 rain and curve (c) to 105 rain irradiation performed at a temperature of 150~C. We found that for an irradiation time equal to 70 rain the glow-curve coincided accurately with curve (a). Using the experimentally determined value of A E = (1.40__+0.02) eV and the value of Tu=22_+0.5 °C estimated from the meteorological data of the region, it was calculated from eq. (7) that the age of the samples is equal to (2300+500)y. The age of the samples based on archaeological evidence 3) corresponds to (2370_+ + 50) y. The main advantage of the proposed method in comparison to the "classical" one, is that a knowledge of the annual dose rate is not essential. Uncertainties in this quantity introduce the most serious errors in classical methods of dating by thermoluminescence. With the method described, we avoid uncertainties that arise from possible supralinearity of the samples4). Of course the method assumes that the sensitivity of the samples does not change with the read-out of the archaeological thermoluminescence. This assumption however is also made in all methods where we have to plot the variation of thermoluminescence with dose, starting from zero.
DATING
The main disadvantage of the method is the assumpt:ion of a good knowledge of the equivalent temperature 7~, of the ground. However, when considering pottery which was buried at great depths or at relatively small depth but in equatorial regions where the annual temperature variations are small, then errors introduced due to T, are negligible. The problem of uncertainties in T u could be solved in cases where we have two or more samples with different A E which have been found at the same location and have the same age. Assuming that small changes in A E affect T~, only slightly so that a common 7~, can be used, then the point of intersection of the lines represented by the equations 111 1a
AE1
kT.
-- Yl ,
(9) AE2
]rl I a - - -
kr.
= 3'2,
which result from the relation (7), gives the archaeolo-
POTTERY
567
gical age of the sample. The experimental confirmation of this last suggestion could be the subject of future study. We conclude by expressing the hope that the method, when perfected, will enlarge the field of archaeological TL dating to include the enormous number of pottery finds at present in museums, for which there is no knowledge of environmental radioactivity. The authors would like to thank Dr. C. Christodoulides for stimulating discussions and comments on the paper. References 1) G. Bonfiglioli, P. Brovetto a n d C. Cortese, Phys. Rev. 114 (1959) 951. 2) j. R. C a m e r o n , D. W. Z i m m e r m a n a n d C. R. Rhyner, in "Thermoluminescence of geological materials" (ed. D. J. M c D o u g a l l ; Academic Press, New York, 1968) p. 471. 3) A. R o m i o p o u l o u , private c o m m u n i c a t i o n . 4) S, J. Fleming, A r c h a e o m e t r y 12 (1970) 135. 5) j. T. Randall a n d W. A. F. Wilkins, Proc. Roy. Soc. (London) (A) 184 (1945) 366.
INSTRUMENTS
AND
METHODS
I37
(I976) 565-567;
©
NORTH-HOLLAND
PUBLISHING
CO.
A NEW M E T H O D OF DATING P O T T E R Y BY T H E R M O L U M I N E S C E N C E STEF. C H A R A L A M B O U S
and CHR. MICHAEL
Department of Nuclear Physics, Aristotle University of Thessaloniki, Greece Received 20 April 1976 T h e shape o f the t h e r m o l u m i n e s c e n c e glow-curve o f an archaeological sample depends on its archaeological age. In this work it is d e m o n s t r a t e d that it is possible to obtain in the laboratory a n artificial glow curve identical to the archaeological one. F r o m the conditions o f the laboratory experiment (temperature o f irradiation a n d dose rate), u n d e r which the identity is achieved, it is possible to estimate the archaeological age o f the sample. T h e theory o f the m e t h o d is presented a n d experimental results are given.
1. Introduction
Thermoluminescence is used in a variety of ways for dating geological and archaeological samples. In the present paper, a method of dating ancient pottery is proposed that is based on the study of the shape and properties of the thermoluminescence glow-curve. The physics of the proposed method is as follows: The pottery sample from the time of its baking until the moment of measurement is continually irradiated (a) by its own radioactivity, (b) by the radioactivity of its environment and (c) by cosmic radiation. We call all these radiations archaeological irradiation. The archaeological irradiation is obviously done at the temperature of the archaeological site (at the exact position of the sample). We call this the archaeological temperature. The above processes have two results: a) an increase of the thermoluminescence with dose (.and time) and, b) a decrease of thermoluminescence due to the escape of trapped electrons on account of their thermal motion at the archaeological temperature. The part of the glow-curve affected is that at low temperatures. This is shown explicitly in fig. 1 where the archaeological glow-curve is shown [curve (a)], and also the glow-curve of the sample after a short and intense irradiation at room temperature [curve (A)], which was taken a few hours later. We found that a glow-curve could be taken, with shape identical to that of the archaeological glow-curve, provided the sample was irradiated rapidly with the archaeological dose but at a temperature suitably higher than the archaeological. In cases where a successful coincidence of the archaeological glow-curve with an "equivalent laboratory glow-curve" was possible, the archaeological age of the sample could be found. As is shown below,
the variable parameters that enter into the problem are only the pair: duration and temperature of irradiation in the laboratory.
I
I
~n 4,,
.0 al
e u c o o c
jm~,
E
o /
b
b (3s') ---./ I I I
t'/
100 Temperature
black body" 200 (°C)
Fig. 1. Glow-curves o f the lerissos pottery. C u r v e (a) is the " a r c h a e o l o g i c a l " glow-curve, a n d (A) that o f a recent short a n d intense irradiation at r o o m temperature a n d to the s a m e total dose. Glow-curves similar to the archaeological one can be obtained if the sample is irradiated to the s a m e dose in a short time at a suitably high temperature. Such a curve (a) was obtained at 150 °C in 70 min. Curves (b) a n d (c) resulted f r o m irradiations at 150°C for 35 and 105 min respectively.
566
STEF.
CHARALAMBOUS
2. Theory and experimental results
(1)
where O is the height of the glow-curve at a certain temperature and f ( O ) a function of O that can be considered constant for a wide range of values of O, but different for different points on the glow-curve. The value of fl was found to be constant and the same for all points on the glow-curve. The relation representing decay by second order kinetics is ~) -dNi/dt
= exp(-E/kT) NinPi,
(2)
where Ni is the number of recombination centers (hole traps) which remain vacant and which correspond to the considered point of the glow-curve, and n is the number of trapped electrons. Pi is a probability factor. Comparison of eq. (2) with the experimentally found relation (1), assuming that O is proportional to Ni, gives f l = E / k and f ( O ) = Pin. Under conditions of constant intensity of radiation, the net change of O with time would be given by the relation: dO =aa(O)dt-f(O)
e x p ( - f l / T ) O dr,
(3)
where ~ represents the dose rate. This is the ratio of the total dose 3 divided by the irradiation time t: i.e. ~ = A/t. The function a(6)) is a function of 6) that gives the increase of thermoluminescence per unit dose (without decay). In the case of linear increase of thermoluminescence with dose, a ( O ) is constant. If e x p ( - f l / T ) = c then eq. (3) can be written as: d O = A a(6)) d(ct) - 1"(6)) 6) d(ct).
(4)
ct
The general solution of the differential eq, (4) would be: 0 = eb(A,ct).
(5)
The physical meaning of eq. (5) is that O, on the basis of the above assumption, will be a function of the total dose A and of ct, and independent of the intensity of radiation (dose rate). This means that for the same dose we can have several pairs ca t~, c2t2 . . . . . cit i for wich c I t I = C2t 2 . . . . .
CHR.
MICHAEL
or
For the archaeological pottery from lerissos in Chalkidiki (Greece) that we had at our disposal, it was found experimentally that the decrease of thermoluminescence with time at temperature T, is given by the following relation: dO/dr = - O . J (O) e x p ( - / ] / T ) ,
AND
(6)
t, e x p ( - A E / k T , )
= t~, e x p ( - A E / k T . ) .
(7)
where t ~ is the duration of irradiation in the laboratory and Tt the temperature of irradiation in the laboratory. and for which pairs we have coincidence of the glowcurves. T~, is the "equivalent" temperature of the sample during the time it was buried at the archaeological site. The value of T. is given to a good approximation by the equation: e At:/kT,
=
(e-AE/k~t,
+ e-AE/k'12 + ... + e
'lC/kT"-)/12
,
(8) where T~, T 2 are the mean temperatures of the ground at the depth where the pottery was found, for each of the 12 months of the year. In eq. (7), t~ is the archaeological age. Eq. (7) is the base of the proposed method. The quantities tj and Tj can be measured with great accuracy in the laboratory. A E can be measured by the method proposed by Cameron et al.Z). T~ is estimated from the meteorological data of the region. The measurement technique and analysis of the data will be presented in a more detailed paper. The method described above was applied to pottery samples from lerissos. Typical curves are shown in fig. 1. Curve (a) is the archaeological curve. Curve (b) corresponds to 35 rain and curve (c) to 105 rain irradiation performed at a temperature of 150~C. We found that for an irradiation time equal to 70 rain the glow-curve coincided accurately with curve (a). Using the experimentally determined value of A E = (1.40__+0.02) eV and the value of Tu=22_+0.5 °C estimated from the meteorological data of the region, it was calculated from eq. (7) that the age of the samples is equal to (2300+500)y. The age of the samples based on archaeological evidence 3) corresponds to (2370_+ + 50) y. The main advantage of the proposed method in comparison to the "classical" one, is that a knowledge of the annual dose rate is not essential. Uncertainties in this quantity introduce the most serious errors in classical methods of dating by thermoluminescence. With the method described, we avoid uncertainties that arise from possible supralinearity of the samples4). Of course the method assumes that the sensitivity of the samples does not change with the read-out of the archaeological thermoluminescence. This assumption however is also made in all methods where we have to plot the variation of thermoluminescence with dose, starting from zero.
DATING
The main disadvantage of the method is the assumpt:ion of a good knowledge of the equivalent temperature 7~, of the ground. However, when considering pottery which was buried at great depths or at relatively small depth but in equatorial regions where the annual temperature variations are small, then errors introduced due to T, are negligible. The problem of uncertainties in T u could be solved in cases where we have two or more samples with different A E which have been found at the same location and have the same age. Assuming that small changes in A E affect T~, only slightly so that a common 7~, can be used, then the point of intersection of the lines represented by the equations 111 1a
AE1
kT.
-- Yl ,
(9) AE2
]rl I a - - -
kr.
= 3'2,
which result from the relation (7), gives the archaeolo-
POTTERY
567
gical age of the sample. The experimental confirmation of this last suggestion could be the subject of future study. We conclude by expressing the hope that the method, when perfected, will enlarge the field of archaeological TL dating to include the enormous number of pottery finds at present in museums, for which there is no knowledge of environmental radioactivity. The authors would like to thank Dr. C. Christodoulides for stimulating discussions and comments on the paper. References 1) G. Bonfiglioli, P. Brovetto a n d C. Cortese, Phys. Rev. 114 (1959) 951. 2) j. R. C a m e r o n , D. W. Z i m m e r m a n a n d C. R. Rhyner, in "Thermoluminescence of geological materials" (ed. D. J. M c D o u g a l l ; Academic Press, New York, 1968) p. 471. 3) A. R o m i o p o u l o u , private c o m m u n i c a t i o n . 4) S, J. Fleming, A r c h a e o m e t r y 12 (1970) 135. 5) j. T. Randall a n d W. A. F. Wilkins, Proc. Roy. Soc. (London) (A) 184 (1945) 366.