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A uniform scale for reporting low-level tritium measurements in water
Irrr. J. Appl.
Rudrtrr.
Iwl.
Vol. 33. pp. 377 to ML 19X2
0020-70xx~x~.050377-06s03.00.0 PergamonPrer\Ltd
Pilntcd I"GreatRr~lam
A Uniform Scale for Reporting Low-Level Tritium Measurements in Water CLAUDE
B. TAYLOR’
and WOLFGANG
‘Institute of Nuclear Sciences, Department of Scientific and Industrial ‘Institut fur Umweltphysik, Universitlt Heidelberg, Heidelberg, (Recwed
ROETHER’ Research, Lower Hutt, New Zealand Federal Republic of Germany
18 June 1981)
To promote uniformity in the calibration and reporting of low-level tritium assays in waters. a tritium measurement scale is proposed for adoption in both b-particle counting and ‘He ingrowth massspectrometric methods- the scale is based on the certified specific activity of the new U.S. National Bureau of Standards tritiated-water standard SRM-4926C (3.406 x lo6 Bq.kg-L ’ on 3 Seotember 1978) and a half life of tritium of 4540days (12.43 yr). For the mass spectrometric method. the new scale replaces that based on the 3He/4He ratio and ‘He concentration in air. but routine calibrations are still made using these parameters. To assist in application of the new scale, equations are developed for calibrating tritium assays by both methods. and for converting results based on earlier measurement scales. The ICRU 1963 recommendation to express tritium concentrations as Tritium Ratios (TR) rather than Tritium Units (TU) is recommended for use with the new measurement scale. but a conversion factor to SI specific activity units (Bq.kgg i) is listed
1. Introduction FOLLOWING a consultants’ meeting convened during September 1979 at the International Atomic Energy Agency (Vienna) to discuss low-level tritium measurement techniques. we were requested to recommend a tritium measurement scale suitable for general adoption by laboratories engaged in low level assays of tritium in environmental waters. Problems of nomenclature and adoption of differing tritium half-life values were already raised by MOGHI~SI”) in 1971. In a recent inter-laboratory tritium comparison.‘2’ a wide variety of tritiated-water standards. half-life values and calibration procedures were used by the participating laboratories. To add to the problem. it is common practice to report tritium data without any mention of the calibration parameters and calculation procedures used. To remedy this situation. we propose the adoption of a uniform scale. to allow tritium measurements to be conducted and reported in such a way that results are strictly intercomparable. The present paper is written with this aim in view, in compliance with the above request. We further believe that the time is opportune for this undertaking. for the following reasons: (a) the most commonly used tritiated-water standard has been the U.S. National Bureau of Standards (NBS) standard SRM-4926.‘3’ When stocks of this standard were exhausted in 1976. it was replaced by an interim standard SRM-4926B. The older (1961) NBS standards were recalibrated in 1978. and new standards prepared and calibrated.‘“’ which are now available from NBS:
(b) The recently developed mass-spectrometric (‘He ingrowth) tritium assay method.t5’ which is likely to be adopted by several laboratories in the near future. has used the 3Hei4He ratio and 4He concentration in air as calibration parameters, thereby introducing a new type of standard for tritium calibration: (c) As regards half-life. the NBS group recently reported a value (12.43 + 0.05) yr based on repeated measurement of their 1961 tritiated-water standards over an 18-yr period. t4’ This and other evidence indicate that the value 12.262 yrc6’ adopted by many environmental tritium laboratories’2) is too short, As an aid to uniformly correct application of the proposed scale, we develop rigorous equations for tritium calibrations and inter-scale corrections, in a form readily applicable to both measurement methods. However. for the experienced tritium scientist. the essential contents reduce to a few brief sections and formulae. to be indicated in summary at the end of the paper. Whereas for most laboratories a change to the new scale will involve only a small adjustment to the applied half-life value (<2:,,), results may shift by several percent within the long periods (up to 2yr) between calibration dates of old and new tritiatedwater standards; these corrections are significant relative to the precision quoted for single measurements (often better than *5”,,).
2. Measurement
Units
In environmental studies. low-level tritium concentrations in waters have usually been reported in TU 377
C. B. Err/or crticiCt!Rorthrr
378
(Tritium Units) at the date of sample collection (I,), where 1 TU corresponds to a T/H ratio of lo-i8. Although the inconsistency of using the term “Unit” for a dimensionless ratio has long been recognised, the 1963 recommendation of the International Commission on Radiation Unitst7i to use instead the term Tritium Ratio (TR) has not been generally followed. But the change is just one of nomenclature and not of scale; TU and TR are completely synonymous and the values remain unchanged. We shall use TR in the following treatment, and we recommend its general adoption in preference to TU; the built-in constant (IO- I*) in the definition of TR is clearly understood by scientists working in this field. We do not favour a change to SI units in environmental water studies. because this would impose difficulty in relating new measurements to the very large body of data already published and well-understood in TU. Tritiated-water standards arc calibrated in specific activity units with symbol (I (Bq. kg- ’ of pure water). Conversion to a Tritium Ratio R is achieved using
R = 10’a ;;_
(1)
where M = molecular weight of the water (kg.mol~ ‘) L = Avogadro constant = 6.02205 x 1023(mol-i) i. = assigned tritium decay constant (s- ’ ) = In 2/T; T+ = assigned tritium half-life (s). A tritium half-life value must therefore be assigned to convert from a to R. Later in this paper, we shall develop equations for tritium assays and calibrations using the tritium concentration N (tritium atoms per kg of pure water). which is directly proportional to R. This avoids repetitive use of the constants in equation (1) during the equation development. Conversion from N to R or (1 is achieved using
N
=
lo-‘”
__ 2;R=;
(la)
3. Choice of Tritium Scale Parameters 3.1 NBS tritiated-wuter
,standards
We consider that the NBS standards are the most accurately calibrated of available tritiated-water standards. The new SRM-4926C standardc4’ is a dilution of a higher-level standard SRM-4927B: SRM-4926C is available in 18 ml aliquots containing adequate activity for preparation of the diluted laboratory substandards (counter calibrations, electrolytic enrichment “spike” waters, 3He ingrowth calibrations) required by low-level laboratories.
TABLF 1, NBS tritiated-water standards Specific activities certified at r0 = 3 September 1978
Standard SRM-4927 SRM-4927B SRM-4926 SRM-4926B SRM-4926C
Quantity per vial Year of issue (ml) 1961 1978 1961 1976 1978
3 3 20 18 18
u,(r,)(Bq.kg (3.411 f (6.909 + (3.406 F (3.402 ) (3.406 +
‘I
0.015) X 0.043) x 0.015) x 0.015) x 0.021) x
1OH IO” IOh IO" IO"
The higher-level standard SRM-4927B has been calibrated (by liquid scintillation counting) against the older standard SRM-4927. which was itself recalibrated in 1978 in the same compensated internal gas counters used for its original calibration in 1961. In this way it was possible to adjust dilution of SRM-4927B so that the resulting daughter-standard SRM-4926C has the same specific activity as the older standard SRM-4926 (daughter-standard of SRM-4927). Details and 1978 calibrations of the various NBS tritiated-water standards are summarised in Table 1. The quoted errors of a, (to) (specific activity of standard at calibration date to) represent the sum of random calibration errors at 99”” C.L. and an estimate of the conceivable systematic errors. The equality of SRM-4926 and SRM-4926C was established by NBS to better than 0.29,.‘” For the attention of laboratories who have used the old standard SRM-4926, we emphasise that the calibration in Table 1 is based on the 1978 measurements.‘“’ and does not derive from the 1961 calibration;“’ the two calibrations are exactly consistent for T, = 12.44 yr.14’ 3.2 Tritium
half-life
We consider that the 12.43 yr half-life determined by the NBS group i4) is the most appropriate value to use in defining a tritium measurement scale; an equivalent choice in SI units is 4540 days exactly. The quoted error (0.05 yr) of the NBS determination is a standard error including all known systematic errors: their half-life value is thus clearly inconsistent with the half-life 12.262 yr commonly applied in many environmental tritium laboratories. In particular. we prefer the NBS value to the value 12.35 yr which has been widely applied in other fields;(8’ our reason for this preference is that the NBS value IS presently the most consistent determination. being obtained in a manner appropriate to the tritium scale problem (a series of measurements on one water sample over an 18-yr period). whereas the 12.35 yr value is a composite value based on determinations of varying type and precision. 3.3 Proposed tritiunl
scalr
Based on the foregoing considerations. ommend the following tritium scale:
we rec-
NBS-4926C is adopted with parameters
as the primary
standard
a,(~,) = 3.406 x lo6 Bq. kg- 1 t,, = 3 September 1978 Ti = 4540 days = 3.92256 x 10’s. These parameters yield the values and conversion Iv = 0.018015 kg.mol ~‘, i 1 TR 1 TR 1 Bq kg - ’
following factors.
assigned using
= 1.7671 x 10-9sm’ = 6.686 x 10’ tritium atoms’kg-’ z 3.193 pCi.kg-’ = 8.464 TR
The last of these conversion factors allows conversion from TR to SI units. We emphasise that the chosen scale parameters are fixed values. Tritium results based on this scale should not include any errors applied to u,(t,,) or T;. However. dilution errors in preparing laboratory substandards from SRM-4926C should be included in assessment of the overall uncertainty of routine measurements. The same measurement scale can also be applied to other hydrogen compounds: this is achieved quite easily by converting a,(t,) for the primary tritiated water standard to a:(t,,) in units Bq~(mol.HJ’ tr;(to) = 6.136 x 104Bq.(mol.Hz)~’ at 3 September
where I, is the starting time of the accumulation period At. Equation (2) is a general formula applicable to both methods.
When obtained standard,
the experimental calibration factor is from measurement of a tritiated-water equation (2) can be developed to give S(r,. At)
where the subscripts .s refer to the standard sample and to is its calibration date. Equation (3) shows that the measured value N(t,) depends on three parameters N,(r,). r. and i ~-~~which are not determined by the measuring laboratory: the values assigned to these parameters uniquely define the tritium measurement scale.
1978
The chosen scale parameters are judged to be of sufficient accuracy to ensure that adjustments of results to any future scale (based on more precisely determined scale parameters) will be less than l”,, over the next 20yr.
4. Calibration
decays which occurred over the accumulation period Al. The proportionality constant. or calibration factor (f), can be determined by measurement of samples prepared from a tritiated-water standard. The tritium concentration N(r,) of a sample at collection date t, is calculated using
Any discrepancy between decay rates based on assigned decay constant i. and actual decay rates. produces a steady drift of scale-determined concentrations N(r,.) relative to the true concentrations ,q(t,). This may be conveniently represented by the ratio of concentrations
of Tritium Measurements
Before considering separate features of the two tritium measurement methods. we draw attention to their equivalence: both techniques measure accumulated decay products from the tritium in the sample, In one case. a-particles are registered individually as they interact with the counter fillmg material: in the other case. the 3He daughter atoms are stored for later mass-spectrometric analysis. The longer accumulation periods for the latter method (weeks to months) compared to the counting methods (hours to days). usually after prior electrolytic or thermal diffusion enrichment). reflect the poorer detection sensitivity of the mass spectrometer. In both methods. the recorded number of decays is adjusted to produce a signal S per unit mass of water sample. which is proportional to the total number of
RT(t,.)
7. tr,(t,)
N(f‘.)
i
,(f
-,,,I,-,,
-,,,-
t,,,
ti,(t,)
where 7. is the decay constant which accurately reflects the actual decay of both sample and tritiated-water standard. and U,(rO) is the true (as distinct from the assigned) specific activity of the standard. In equation (4). the drift is essentially given by the exponential third factor on the RHS. In most cases fi 2 f,,. and Ar. Ar, are so short that equation (4) can be expressed to first order by N(f,)
= -
.V(f,)
;
.I;$;
[I - (i - i)(f, - lo)].
(4a)
)
The discrepancy between measured and true concentrations is thus a combination of constant. but unknown factors. and a drift term which increases linearly with the period elapsed between standard
380
C. B. Tu~lor und W Roether
calibration date t, and sample collection date t,: the drift amounts to 0.06% per year if 2 differs from j by 1:;. We have shown that the drift effect is an inherent uncertainty in tritium measurements. As a corollary to this. we note that a similar time-drift occurs between measured concentrations based on any two assigned scales with differing decay constants: in this case, however. the relative drift can be precisely determined (see Section 5.2). As a consequence of the drift effect, the relatively short half-life of tritium. and the uncertainty still inherent in the scale parameters. scale adjustments should be reconsidered at intervals of several years. In contrast. the situation does not arise in i4C standardisation. where the half-life is so long that the drift correction (i. - i) (f, - to) in equation (4a) is effectively zero.
constant i. However, in order to obtain a mutually consistent calibration between counting and mass spectrometric methods, we propose also the adoption of a tritiated-water standard as the primary standard in the latter technique. Modifying equation (2). the measurement at date I, of 3He ingrowth from an unknown sample gives
where the subscripts “A” denote air-calibrated measurements. NA(tr) is effectively independent of t, because the varying mass spectrometer response is compensated by the variable sensitivity factor ,f4(tm) obtained from measurement of the interspersed air aliquots (7)
4.4 Ctrlihrclfion irf c’ountin~qmethod In the counting method, both i.Ar and iAt, are invariably so small that the tritium concentration of the sample may be calculated using a simplified form of equation (3).
Here S,,,(r,) is the signal from an air aliquot containing assigned number N,,,, of 3He atoms. Combining (6) and (7) gives
where n(t,). ~i,(r,,) are respectively net count rates per unit mass of water sample (before enrichment) and standard (before dilution). In most laboratories. counts of samples prepared from a diluted tritiated-water standard are made every week or so, because of the inherent changeability of detection efficiency in the operation of lowlevel counting systems. Regular preparation and counting of standard samples monitors these changes, as well as the reproducibility of the sample preparation methods. In these circumstances. ti effectively equals I,,. and equation (5) simplifies further to
Alternatively. a calibration based on a tritiatedwater standard would be obtained if the mass spectrometer sensitivity was determined by admitting ‘He produced by ingrowth from the tritiated-water standard (equation (3) modified to include dependence of signal S on t,). In order to convert air-calibrated results to the tritiated-water standard scale. it suffices to perform a cross-calibration yielding a scale conversion factor
(54
where n,(rJ is usually based on the trend of the regular repeated measurements rather than on a single measurement. This is the calibration equation usually adopted for routine counting measurements. 4.5 Colibrutions in m~~.s.s-spectrometric method In routine mass-spectrometric measurement using the ‘He ingrowth method. air aliquot measurements are interspersed with the sample measurements:“’ this procedure monitors and corrects for short-term changes of “He sensitivity of the mass spectrometer. i.e. air 3He is used as a measurement sub-standard. Air 3He has also been used to calibrate the measurements,(5) the assigned parameters of this scale being the 3He concentration in air (supposed essentially uniform and derived from presently-accepted values for 4He concentration and 3He/4He ratio). and the decay
where N,,5(t,) is determined from samples of “He accumulated from suitably diluted tritiated-water standard. several measurements being required to reach satisfactory precision. This scale conversion factor drifts slowly with time. again by 0.06”,, per year of (r,, - rO) for l”,, difference between assigned and actual rate of decay (cf. Section 4.3). The cross-calibration experiment needs therefore to be repeated only at intervals of some years. In routine measurement, the scale conversion factor of equation (9) is applied to the air-calibrated result N,,(t,).
5. Tritium Scale Conversions A primary aim of this paper is to determine conditions and procedures which allow intercomparability to be established between self-consistent data sets based on different scale parameters.
I 04
I
Correctwn factors from NBS-4926, t$ = 12.262~
NBS-4926C. I 03
to
‘4 = 12 430~
Trltlum ratio Correctfon
1
/.
I 02
I 01
I oc
0.99
0 98 I!
0
I
1950
I
1960
I
1970
I
I
1980 1990
‘cFIG. 1. An example of inter-scale conversion, showing COTrection factors for converting B-counting results from scale defined by 1961 calibration of SRM-4926 (specific activity on 3 September 1961) and half-life 8.780 x lo6 Bq,kg-’ 12.262yr to the new scale based on SRM-4926C (specific activity 3.406 x lo6 Bq.kg- I on 3 September 1978) and half-life 12.43 yr. as a function of sample collection date r, (time divisions refer to 3 September in indicated year).
5.1 Nottrrion In the following sections. starred parameters (e.g. N*(r,), u,*(t,,*), ;.*) refer to a scale that is to replace a previously-used scale (unstarred parameters). 5.2 Genertrl considertrtions coumi)lg
und conversion formultr
for
merhods
To establish conversion of a measured concentration N(t,) to the value N*( t,) on a new scale. we are posing the question: what result would we have obtained if we had used the new tritiated-water standard and decay constant to calibrate the original measurement’? For the sake of directness, we give first the answer for the special case of the counting method (equation 5): the general case can be found by applying equation (3) instead. (Equation (5) yields
This is the scale conversion equation for the counting method, expressing the conversion factor as a function of sampling time Tc.Although we have derived equation (10A) as a general equation for conversion of old data to the new scale, it is of course applicable to interrelate any two sets of data based on different scales: here also a simultaneous comparison or reliable cross-linkage of tritiated-water standards is required. For the special case of NBS standards SRM-4926 and SRM-4926C. the concentration ratio has been established as unity by NBS.14’ For several laboratories, the change to the scale recommended above involves switching between these standards. and from half-life 12.262 to 12.43 yr. We have used this scale switch as an example in Fig. 1, which shows correction factors derived for sample collection date t, ranging from 1940 (earliest conceivable r,) to 1990. Note that the accuracy of these factors is only as good as the equality of specific activity established by NBS for these two standards (apparently better than 0.2”~. We have shown above that precise inter-scale conversion requires simultaneous measurement of the count rate ratio of the two tritiated-water standards. In some cases this may not be possible, e.g. if the old standard is no longer available. Even if the continuity of the detector calibration is accurately established, non-simultaneous standard measurements cannot generally be used if the time gap (tz - t,,) between the measurements is several years or longer: the difficulty lies in the drift effect discussed in Section 4.3. i.e. the uncertainty in the half-life used to bridge the time gap. Therefore there will be cases where inter-scale data conversion cannot be accomplished with appropriate accuracy. 5.3 Concersionformulofor
N,(r,. j.)
(lOa)
data
In the few laboratories presently using the 3He ingrowth technique. previous results have been calculated by equation (8) using the air standard and assigned i. We now incorporate the dependence of the result on i by rewriting N,(t,) as N,(r,. i). Converting to the new scale involves a change from air standard to tritiated-water standard and from i to i* according to
N*(t,. i*) All parameters on the RHS of equation (IO) are measured or defined, with the exception of n,T(ti,). which is the count rate which would have been obtained if the new standard had been used at the time ti, of the original detector calibration. But the ratio of the actual concentrations of the old and new standard is of course invariant with time. Therefore it suffices to determine the ratio n/n,: from simultaneous measurements at any time t. If moreover we assume t II : t, (see Section 4.4). equation (10) simplifies to
muss spectrometric
N*(t,.
i*)
N,(t,. i*)
X,(r,.
i*)
Na(t,. i.)
The procedure for conversion of old data therefore involves a cross-calibration between the air standard and ‘He accumulations from the diluted tritiatedwater standard (see Section 4.5), followed by application of equation (1 I). The availability of the air standard is advantageous. because it allows equation (11) to be applied also in any future change of water standard-based scale, i.e. the corrections are applied to routine. air-calibrated results. The air standard
therefore acts as a calibration link. But, if the continuity of the air standard is uncertain, the restrictions on data correction discussed in Section 5.2 must again be taken
into account.
6. Summary of Recommended We
recommend
that
future
Procedures low-level
tritium
measurements should be reported usmg the scale defined in Section 3.3. The equations for calculating results are equations (5A) and 1A) for counting methods, and (8). (9) and (1A) for the mass spectrometric method. We further suggest that laboratories should establish and report the conversion factors to correct previously released measurements to the new scale. The conversion factors are given by equations (10A) for counting methods and (11) for the mass spectrometric method. Figure 1 is a diagrammatic example of the conversion factors for the indicated special case. A(,~,lo,~/rt/ym~rnr,s We thank Dr T. FLORKOWSKI, Scientific Secretary of the Consultants‘ Group Meeting at IAEA. and the other participants for stimulating this study. The general consensus of the Group w&s that a new tritium scale based on SRM-4926C should be adopted. On the basis of the evidence then available. the Group favoured a half-life choice of 12.35 yr: we have moved now to the
12.43 yr value smce determined by NBS.‘“’ Collected workIng papers and recommendations of the Group Meeting are now available on request from IAEA P.O. Box 100. A-1400 Vienna Austria as TEC DOC-246. This work would not have been accomolished wlthout extensive discussions with the participants’of the Consultan&’ Group. We are particul& giateful to Dr W. B. MANN for sharpening our view towards a straightforward presentation of our ideas. and correct use of units and nomenclature. Comments of Dr J. G. V. TAYLOR and anonymous reviewers on a previous version of the paper were also particularly helpful.
References ‘. MO~;HISSI A. A. Tririum (Eds MO(;HISSI A. A. and CARTER M. W.) Messenger Graphics. 28 (1973). 2. TAYLOR C. B. fnr. J. Appl. Radiar. Isot. 29, 39 (1978). 3. MANN W. B.. MEDLOCK R. W. and YLRA D. Ihiti 15, 35 I (1964). 4. UNTERWEC~ERM. P., COURSEY B. M.. S~HIMA F. J. and MANN W. B. Ibid. 31. 61 1 (1980). 5, CLARKE W. B.. JENKINS W. J and TOP Z. Ihirl. 27, 515 (1976). 6. JONES W. M. Php Rev. 100, 124 (1955). Recommendations of the International 7. “Radioactivity” Commission on Rachological Units and Measurements (1962) Report 1OC NBS Handbook 86. p. viii (Washington DC 1963). of RadioactivIty Measurements and 8. “A Handbook Procedures.’ U.S. National Council on Radiation Protection and Measurements. Report No. 58 (1978).
Rudrtrr.
Iwl.
Vol. 33. pp. 377 to ML 19X2
0020-70xx~x~.050377-06s03.00.0 PergamonPrer\Ltd
Pilntcd I"GreatRr~lam
A Uniform Scale for Reporting Low-Level Tritium Measurements in Water CLAUDE
B. TAYLOR’
and WOLFGANG
‘Institute of Nuclear Sciences, Department of Scientific and Industrial ‘Institut fur Umweltphysik, Universitlt Heidelberg, Heidelberg, (Recwed
ROETHER’ Research, Lower Hutt, New Zealand Federal Republic of Germany
18 June 1981)
To promote uniformity in the calibration and reporting of low-level tritium assays in waters. a tritium measurement scale is proposed for adoption in both b-particle counting and ‘He ingrowth massspectrometric methods- the scale is based on the certified specific activity of the new U.S. National Bureau of Standards tritiated-water standard SRM-4926C (3.406 x lo6 Bq.kg-L ’ on 3 Seotember 1978) and a half life of tritium of 4540days (12.43 yr). For the mass spectrometric method. the new scale replaces that based on the 3He/4He ratio and ‘He concentration in air. but routine calibrations are still made using these parameters. To assist in application of the new scale, equations are developed for calibrating tritium assays by both methods. and for converting results based on earlier measurement scales. The ICRU 1963 recommendation to express tritium concentrations as Tritium Ratios (TR) rather than Tritium Units (TU) is recommended for use with the new measurement scale. but a conversion factor to SI specific activity units (Bq.kgg i) is listed
1. Introduction FOLLOWING a consultants’ meeting convened during September 1979 at the International Atomic Energy Agency (Vienna) to discuss low-level tritium measurement techniques. we were requested to recommend a tritium measurement scale suitable for general adoption by laboratories engaged in low level assays of tritium in environmental waters. Problems of nomenclature and adoption of differing tritium half-life values were already raised by MOGHI~SI”) in 1971. In a recent inter-laboratory tritium comparison.‘2’ a wide variety of tritiated-water standards. half-life values and calibration procedures were used by the participating laboratories. To add to the problem. it is common practice to report tritium data without any mention of the calibration parameters and calculation procedures used. To remedy this situation. we propose the adoption of a uniform scale. to allow tritium measurements to be conducted and reported in such a way that results are strictly intercomparable. The present paper is written with this aim in view, in compliance with the above request. We further believe that the time is opportune for this undertaking. for the following reasons: (a) the most commonly used tritiated-water standard has been the U.S. National Bureau of Standards (NBS) standard SRM-4926.‘3’ When stocks of this standard were exhausted in 1976. it was replaced by an interim standard SRM-4926B. The older (1961) NBS standards were recalibrated in 1978. and new standards prepared and calibrated.‘“’ which are now available from NBS:
(b) The recently developed mass-spectrometric (‘He ingrowth) tritium assay method.t5’ which is likely to be adopted by several laboratories in the near future. has used the 3Hei4He ratio and 4He concentration in air as calibration parameters, thereby introducing a new type of standard for tritium calibration: (c) As regards half-life. the NBS group recently reported a value (12.43 + 0.05) yr based on repeated measurement of their 1961 tritiated-water standards over an 18-yr period. t4’ This and other evidence indicate that the value 12.262 yrc6’ adopted by many environmental tritium laboratories’2) is too short, As an aid to uniformly correct application of the proposed scale, we develop rigorous equations for tritium calibrations and inter-scale corrections, in a form readily applicable to both measurement methods. However. for the experienced tritium scientist. the essential contents reduce to a few brief sections and formulae. to be indicated in summary at the end of the paper. Whereas for most laboratories a change to the new scale will involve only a small adjustment to the applied half-life value (<2:,,), results may shift by several percent within the long periods (up to 2yr) between calibration dates of old and new tritiatedwater standards; these corrections are significant relative to the precision quoted for single measurements (often better than *5”,,).
2. Measurement
Units
In environmental studies. low-level tritium concentrations in waters have usually been reported in TU 377
C. B. Err/or crticiCt!Rorthrr
378
(Tritium Units) at the date of sample collection (I,), where 1 TU corresponds to a T/H ratio of lo-i8. Although the inconsistency of using the term “Unit” for a dimensionless ratio has long been recognised, the 1963 recommendation of the International Commission on Radiation Unitst7i to use instead the term Tritium Ratio (TR) has not been generally followed. But the change is just one of nomenclature and not of scale; TU and TR are completely synonymous and the values remain unchanged. We shall use TR in the following treatment, and we recommend its general adoption in preference to TU; the built-in constant (IO- I*) in the definition of TR is clearly understood by scientists working in this field. We do not favour a change to SI units in environmental water studies. because this would impose difficulty in relating new measurements to the very large body of data already published and well-understood in TU. Tritiated-water standards arc calibrated in specific activity units with symbol (I (Bq. kg- ’ of pure water). Conversion to a Tritium Ratio R is achieved using
R = 10’a ;;_
(1)
where M = molecular weight of the water (kg.mol~ ‘) L = Avogadro constant = 6.02205 x 1023(mol-i) i. = assigned tritium decay constant (s- ’ ) = In 2/T; T+ = assigned tritium half-life (s). A tritium half-life value must therefore be assigned to convert from a to R. Later in this paper, we shall develop equations for tritium assays and calibrations using the tritium concentration N (tritium atoms per kg of pure water). which is directly proportional to R. This avoids repetitive use of the constants in equation (1) during the equation development. Conversion from N to R or (1 is achieved using
N
=
lo-‘”
__ 2;R=;
(la)
3. Choice of Tritium Scale Parameters 3.1 NBS tritiated-wuter
,standards
We consider that the NBS standards are the most accurately calibrated of available tritiated-water standards. The new SRM-4926C standardc4’ is a dilution of a higher-level standard SRM-4927B: SRM-4926C is available in 18 ml aliquots containing adequate activity for preparation of the diluted laboratory substandards (counter calibrations, electrolytic enrichment “spike” waters, 3He ingrowth calibrations) required by low-level laboratories.
TABLF 1, NBS tritiated-water standards Specific activities certified at r0 = 3 September 1978
Standard SRM-4927 SRM-4927B SRM-4926 SRM-4926B SRM-4926C
Quantity per vial Year of issue (ml) 1961 1978 1961 1976 1978
3 3 20 18 18
u,(r,)(Bq.kg (3.411 f (6.909 + (3.406 F (3.402 ) (3.406 +
‘I
0.015) X 0.043) x 0.015) x 0.015) x 0.021) x
1OH IO” IOh IO" IO"
The higher-level standard SRM-4927B has been calibrated (by liquid scintillation counting) against the older standard SRM-4927. which was itself recalibrated in 1978 in the same compensated internal gas counters used for its original calibration in 1961. In this way it was possible to adjust dilution of SRM-4927B so that the resulting daughter-standard SRM-4926C has the same specific activity as the older standard SRM-4926 (daughter-standard of SRM-4927). Details and 1978 calibrations of the various NBS tritiated-water standards are summarised in Table 1. The quoted errors of a, (to) (specific activity of standard at calibration date to) represent the sum of random calibration errors at 99”” C.L. and an estimate of the conceivable systematic errors. The equality of SRM-4926 and SRM-4926C was established by NBS to better than 0.29,.‘” For the attention of laboratories who have used the old standard SRM-4926, we emphasise that the calibration in Table 1 is based on the 1978 measurements.‘“’ and does not derive from the 1961 calibration;“’ the two calibrations are exactly consistent for T, = 12.44 yr.14’ 3.2 Tritium
half-life
We consider that the 12.43 yr half-life determined by the NBS group i4) is the most appropriate value to use in defining a tritium measurement scale; an equivalent choice in SI units is 4540 days exactly. The quoted error (0.05 yr) of the NBS determination is a standard error including all known systematic errors: their half-life value is thus clearly inconsistent with the half-life 12.262 yr commonly applied in many environmental tritium laboratories. In particular. we prefer the NBS value to the value 12.35 yr which has been widely applied in other fields;(8’ our reason for this preference is that the NBS value IS presently the most consistent determination. being obtained in a manner appropriate to the tritium scale problem (a series of measurements on one water sample over an 18-yr period). whereas the 12.35 yr value is a composite value based on determinations of varying type and precision. 3.3 Proposed tritiunl
scalr
Based on the foregoing considerations. ommend the following tritium scale:
we rec-
NBS-4926C is adopted with parameters
as the primary
standard
a,(~,) = 3.406 x lo6 Bq. kg- 1 t,, = 3 September 1978 Ti = 4540 days = 3.92256 x 10’s. These parameters yield the values and conversion Iv = 0.018015 kg.mol ~‘, i 1 TR 1 TR 1 Bq kg - ’
following factors.
assigned using
= 1.7671 x 10-9sm’ = 6.686 x 10’ tritium atoms’kg-’ z 3.193 pCi.kg-’ = 8.464 TR
The last of these conversion factors allows conversion from TR to SI units. We emphasise that the chosen scale parameters are fixed values. Tritium results based on this scale should not include any errors applied to u,(t,,) or T;. However. dilution errors in preparing laboratory substandards from SRM-4926C should be included in assessment of the overall uncertainty of routine measurements. The same measurement scale can also be applied to other hydrogen compounds: this is achieved quite easily by converting a,(t,) for the primary tritiated water standard to a:(t,,) in units Bq~(mol.HJ’ tr;(to) = 6.136 x 104Bq.(mol.Hz)~’ at 3 September
where I, is the starting time of the accumulation period At. Equation (2) is a general formula applicable to both methods.
When obtained standard,
the experimental calibration factor is from measurement of a tritiated-water equation (2) can be developed to give S(r,. At)
where the subscripts .s refer to the standard sample and to is its calibration date. Equation (3) shows that the measured value N(t,) depends on three parameters N,(r,). r. and i ~-~~which are not determined by the measuring laboratory: the values assigned to these parameters uniquely define the tritium measurement scale.
1978
The chosen scale parameters are judged to be of sufficient accuracy to ensure that adjustments of results to any future scale (based on more precisely determined scale parameters) will be less than l”,, over the next 20yr.
4. Calibration
decays which occurred over the accumulation period Al. The proportionality constant. or calibration factor (f), can be determined by measurement of samples prepared from a tritiated-water standard. The tritium concentration N(r,) of a sample at collection date t, is calculated using
Any discrepancy between decay rates based on assigned decay constant i. and actual decay rates. produces a steady drift of scale-determined concentrations N(r,.) relative to the true concentrations ,q(t,). This may be conveniently represented by the ratio of concentrations
of Tritium Measurements
Before considering separate features of the two tritium measurement methods. we draw attention to their equivalence: both techniques measure accumulated decay products from the tritium in the sample, In one case. a-particles are registered individually as they interact with the counter fillmg material: in the other case. the 3He daughter atoms are stored for later mass-spectrometric analysis. The longer accumulation periods for the latter method (weeks to months) compared to the counting methods (hours to days). usually after prior electrolytic or thermal diffusion enrichment). reflect the poorer detection sensitivity of the mass spectrometer. In both methods. the recorded number of decays is adjusted to produce a signal S per unit mass of water sample. which is proportional to the total number of
RT(t,.)
7. tr,(t,)
N(f‘.)
i
,(f
-,,,I,-,,
-,,,-
t,,,
ti,(t,)
where 7. is the decay constant which accurately reflects the actual decay of both sample and tritiated-water standard. and U,(rO) is the true (as distinct from the assigned) specific activity of the standard. In equation (4). the drift is essentially given by the exponential third factor on the RHS. In most cases fi 2 f,,. and Ar. Ar, are so short that equation (4) can be expressed to first order by N(f,)
= -
.V(f,)
;
.I;$;
[I - (i - i)(f, - lo)].
(4a)
)
The discrepancy between measured and true concentrations is thus a combination of constant. but unknown factors. and a drift term which increases linearly with the period elapsed between standard
380
C. B. Tu~lor und W Roether
calibration date t, and sample collection date t,: the drift amounts to 0.06% per year if 2 differs from j by 1:;. We have shown that the drift effect is an inherent uncertainty in tritium measurements. As a corollary to this. we note that a similar time-drift occurs between measured concentrations based on any two assigned scales with differing decay constants: in this case, however. the relative drift can be precisely determined (see Section 5.2). As a consequence of the drift effect, the relatively short half-life of tritium. and the uncertainty still inherent in the scale parameters. scale adjustments should be reconsidered at intervals of several years. In contrast. the situation does not arise in i4C standardisation. where the half-life is so long that the drift correction (i. - i) (f, - to) in equation (4a) is effectively zero.
constant i. However, in order to obtain a mutually consistent calibration between counting and mass spectrometric methods, we propose also the adoption of a tritiated-water standard as the primary standard in the latter technique. Modifying equation (2). the measurement at date I, of 3He ingrowth from an unknown sample gives
where the subscripts “A” denote air-calibrated measurements. NA(tr) is effectively independent of t, because the varying mass spectrometer response is compensated by the variable sensitivity factor ,f4(tm) obtained from measurement of the interspersed air aliquots (7)
4.4 Ctrlihrclfion irf c’ountin~qmethod In the counting method, both i.Ar and iAt, are invariably so small that the tritium concentration of the sample may be calculated using a simplified form of equation (3).
Here S,,,(r,) is the signal from an air aliquot containing assigned number N,,,, of 3He atoms. Combining (6) and (7) gives
where n(t,). ~i,(r,,) are respectively net count rates per unit mass of water sample (before enrichment) and standard (before dilution). In most laboratories. counts of samples prepared from a diluted tritiated-water standard are made every week or so, because of the inherent changeability of detection efficiency in the operation of lowlevel counting systems. Regular preparation and counting of standard samples monitors these changes, as well as the reproducibility of the sample preparation methods. In these circumstances. ti effectively equals I,,. and equation (5) simplifies further to
Alternatively. a calibration based on a tritiatedwater standard would be obtained if the mass spectrometer sensitivity was determined by admitting ‘He produced by ingrowth from the tritiated-water standard (equation (3) modified to include dependence of signal S on t,). In order to convert air-calibrated results to the tritiated-water standard scale. it suffices to perform a cross-calibration yielding a scale conversion factor
(54
where n,(rJ is usually based on the trend of the regular repeated measurements rather than on a single measurement. This is the calibration equation usually adopted for routine counting measurements. 4.5 Colibrutions in m~~.s.s-spectrometric method In routine mass-spectrometric measurement using the ‘He ingrowth method. air aliquot measurements are interspersed with the sample measurements:“’ this procedure monitors and corrects for short-term changes of “He sensitivity of the mass spectrometer. i.e. air 3He is used as a measurement sub-standard. Air 3He has also been used to calibrate the measurements,(5) the assigned parameters of this scale being the 3He concentration in air (supposed essentially uniform and derived from presently-accepted values for 4He concentration and 3He/4He ratio). and the decay
where N,,5(t,) is determined from samples of “He accumulated from suitably diluted tritiated-water standard. several measurements being required to reach satisfactory precision. This scale conversion factor drifts slowly with time. again by 0.06”,, per year of (r,, - rO) for l”,, difference between assigned and actual rate of decay (cf. Section 4.3). The cross-calibration experiment needs therefore to be repeated only at intervals of some years. In routine measurement, the scale conversion factor of equation (9) is applied to the air-calibrated result N,,(t,).
5. Tritium Scale Conversions A primary aim of this paper is to determine conditions and procedures which allow intercomparability to be established between self-consistent data sets based on different scale parameters.
I 04
I
Correctwn factors from NBS-4926, t$ = 12.262~
NBS-4926C. I 03
to
‘4 = 12 430~
Trltlum ratio Correctfon
1
/.
I 02
I 01
I oc
0.99
0 98 I!
0
I
1950
I
1960
I
1970
I
I
1980 1990
‘cFIG. 1. An example of inter-scale conversion, showing COTrection factors for converting B-counting results from scale defined by 1961 calibration of SRM-4926 (specific activity on 3 September 1961) and half-life 8.780 x lo6 Bq,kg-’ 12.262yr to the new scale based on SRM-4926C (specific activity 3.406 x lo6 Bq.kg- I on 3 September 1978) and half-life 12.43 yr. as a function of sample collection date r, (time divisions refer to 3 September in indicated year).
5.1 Nottrrion In the following sections. starred parameters (e.g. N*(r,), u,*(t,,*), ;.*) refer to a scale that is to replace a previously-used scale (unstarred parameters). 5.2 Genertrl considertrtions coumi)lg
und conversion formultr
for
merhods
To establish conversion of a measured concentration N(t,) to the value N*( t,) on a new scale. we are posing the question: what result would we have obtained if we had used the new tritiated-water standard and decay constant to calibrate the original measurement’? For the sake of directness, we give first the answer for the special case of the counting method (equation 5): the general case can be found by applying equation (3) instead. (Equation (5) yields
This is the scale conversion equation for the counting method, expressing the conversion factor as a function of sampling time Tc.Although we have derived equation (10A) as a general equation for conversion of old data to the new scale, it is of course applicable to interrelate any two sets of data based on different scales: here also a simultaneous comparison or reliable cross-linkage of tritiated-water standards is required. For the special case of NBS standards SRM-4926 and SRM-4926C. the concentration ratio has been established as unity by NBS.14’ For several laboratories, the change to the scale recommended above involves switching between these standards. and from half-life 12.262 to 12.43 yr. We have used this scale switch as an example in Fig. 1, which shows correction factors derived for sample collection date t, ranging from 1940 (earliest conceivable r,) to 1990. Note that the accuracy of these factors is only as good as the equality of specific activity established by NBS for these two standards (apparently better than 0.2”~. We have shown above that precise inter-scale conversion requires simultaneous measurement of the count rate ratio of the two tritiated-water standards. In some cases this may not be possible, e.g. if the old standard is no longer available. Even if the continuity of the detector calibration is accurately established, non-simultaneous standard measurements cannot generally be used if the time gap (tz - t,,) between the measurements is several years or longer: the difficulty lies in the drift effect discussed in Section 4.3. i.e. the uncertainty in the half-life used to bridge the time gap. Therefore there will be cases where inter-scale data conversion cannot be accomplished with appropriate accuracy. 5.3 Concersionformulofor
N,(r,. j.)
(lOa)
data
In the few laboratories presently using the 3He ingrowth technique. previous results have been calculated by equation (8) using the air standard and assigned i. We now incorporate the dependence of the result on i by rewriting N,(t,) as N,(r,. i). Converting to the new scale involves a change from air standard to tritiated-water standard and from i to i* according to
N*(t,. i*) All parameters on the RHS of equation (IO) are measured or defined, with the exception of n,T(ti,). which is the count rate which would have been obtained if the new standard had been used at the time ti, of the original detector calibration. But the ratio of the actual concentrations of the old and new standard is of course invariant with time. Therefore it suffices to determine the ratio n/n,: from simultaneous measurements at any time t. If moreover we assume t II : t, (see Section 4.4). equation (10) simplifies to
muss spectrometric
N*(t,.
i*)
N,(t,. i*)
X,(r,.
i*)
Na(t,. i.)
The procedure for conversion of old data therefore involves a cross-calibration between the air standard and ‘He accumulations from the diluted tritiatedwater standard (see Section 4.5), followed by application of equation (1 I). The availability of the air standard is advantageous. because it allows equation (11) to be applied also in any future change of water standard-based scale, i.e. the corrections are applied to routine. air-calibrated results. The air standard
therefore acts as a calibration link. But, if the continuity of the air standard is uncertain, the restrictions on data correction discussed in Section 5.2 must again be taken
into account.
6. Summary of Recommended We
recommend
that
future
Procedures low-level
tritium
measurements should be reported usmg the scale defined in Section 3.3. The equations for calculating results are equations (5A) and 1A) for counting methods, and (8). (9) and (1A) for the mass spectrometric method. We further suggest that laboratories should establish and report the conversion factors to correct previously released measurements to the new scale. The conversion factors are given by equations (10A) for counting methods and (11) for the mass spectrometric method. Figure 1 is a diagrammatic example of the conversion factors for the indicated special case. A(,~,lo,~/rt/ym~rnr,s We thank Dr T. FLORKOWSKI, Scientific Secretary of the Consultants‘ Group Meeting at IAEA. and the other participants for stimulating this study. The general consensus of the Group w&s that a new tritium scale based on SRM-4926C should be adopted. On the basis of the evidence then available. the Group favoured a half-life choice of 12.35 yr: we have moved now to the
12.43 yr value smce determined by NBS.‘“’ Collected workIng papers and recommendations of the Group Meeting are now available on request from IAEA P.O. Box 100. A-1400 Vienna Austria as TEC DOC-246. This work would not have been accomolished wlthout extensive discussions with the participants’of the Consultan&’ Group. We are particul& giateful to Dr W. B. MANN for sharpening our view towards a straightforward presentation of our ideas. and correct use of units and nomenclature. Comments of Dr J. G. V. TAYLOR and anonymous reviewers on a previous version of the paper were also particularly helpful.
References ‘. MO~;HISSI A. A. Tririum (Eds MO(;HISSI A. A. and CARTER M. W.) Messenger Graphics. 28 (1973). 2. TAYLOR C. B. fnr. J. Appl. Radiar. Isot. 29, 39 (1978). 3. MANN W. B.. MEDLOCK R. W. and YLRA D. Ihiti 15, 35 I (1964). 4. UNTERWEC~ERM. P., COURSEY B. M.. S~HIMA F. J. and MANN W. B. Ibid. 31. 61 1 (1980). 5, CLARKE W. B.. JENKINS W. J and TOP Z. Ihirl. 27, 515 (1976). 6. JONES W. M. Php Rev. 100, 124 (1955). Recommendations of the International 7. “Radioactivity” Commission on Rachological Units and Measurements (1962) Report 1OC NBS Handbook 86. p. viii (Washington DC 1963). of RadioactivIty Measurements and 8. “A Handbook Procedures.’ U.S. National Council on Radiation Protection and Measurements. Report No. 58 (1978).