Ir544 Barium sulphate method for consecutive determination of radium-226 and radium-228 on the same source

3 Method calibration and results

3.1 Gamma spectrometry method calibration

3.1.1 Efficiency determination

5 sealed standards were prepared and counted to determine the efficiency of the detection system at the 911 and 969 keV peaks of ²²⁸Ac. ²²⁸Ac was allowed sufficient time to equilibrate with ²²⁸Ra. Table 4 shows the activity of the standards, net count rates and the calculated efficiency for each standard disc at each peak. The peak decay probability (PDP) for the 911 keV peak is 26.6%, and combined PDP for the doublet peak at 969 keV is 20.45% (Martin & Hancock 2004b).

Table 4 Efficiency calibration data

Standard disc activity (Bq)	911 keV (net counts per kilosecond)	969 keV (net counts per kilosecond)	Efficiency at 911 keV (%)	Efficiency at 969 keV (%)
55.7	401	310	2.71	2.72
40.6	295	233	2.73	2.81
21.3	153	120	2.70	2.75
11.4	81.1	64.0	2.67	2.74
8.42	56.8	44.9	2.54	2.60

Efficiency was determined using Equation 9.

Gamma decay line efficiency determination. Equation 9

Where –

ε_Peak – The efficiency in the peak of interest

C_Peak – The gross counts in the peak

B_L– The background counts in a region to the left of the gamma line spanning half the width of the main region of interest

B_R – The background counts in a region to the right of the gamma line spanning half the width of the main region of interest

PDP_c – The Combined Peak Decay Probability of the 911 and 969 keV which is 0.4705

A_Std – The ²²⁸Ra activity of the standard disc

t – Count time (kiloseconds)

Average efficiency and standard deviation for each peak was 2.67±0.08 and 2.72±0.07 for the 911 and 969 keV peaks respectively. Due to the negligible difference between the efficiency calculated for the 2 peaks, a combined efficiency for both peaks was determined, using a combined average of all efficiencies calculated for each peak for each standard, to be 2.70%, with a standard deviation of 0.08%. Figure 8 shows net count rates of all sealed standards versus activity of those standards.

Figure 8 Combined net count rates of ²²⁸Ac decay lines at 911 and 969 keV of sealed standards vs. activity of sealed standards

The R² value of 0.999 indicates clear correlation between activity of the standards and the net count rates across a wide range of activities. The apparently negative intercept signified in the equation from Figure 8 is not statistically significantly different from zero (p=0.54).


²²⁸Ac lines at 911 and 969 keV

Figure 9 HPGe gamma spectrum of the most active of the sealed standards. No additional lines close to the 911 and 969 keV lines of ²²⁸Ac can be seen, even in the logarithmic scale.

Comparison of the separated ²²⁸Ra spectra (see Figure 9) with those of the sealed standards also showed that the assumptions of no interference in the ²²⁸Ac lines from ²³²Th or daughters in secular equilibrium were correct.

In addition a clean PVDF sample holder and chemical blanks prepared with the sealed and unsealed standards, and ¹³³Ba blanks with increasing volumes of ¹³³Ba tracer ranging from 1/20 of that used in normal samples (Ba-133 Blank #1) to an equal volume as that used in normal samples (Ba-133 Blank #5). No upward trend in count rates in the combined 911 and 969 peaks was observed, and no significant variations, within uncertainty, in the count rates of the blanks can be observed when compared with that of the blank PVDF sample holder (Table 5).

Table 5 Blank count rates after Compton and natural background subtraction of various blanks

Blank type	Count rate (counts per kilosecond) in 911 and 969 keV peaks	Uncertainty (counts per kilosecond)
Blank PVDF sample holder	0.524	0.141
Sealed standard Chemical Blank, average of 2 counts	0.309	0.135
Unsealed standard Chemical Blank, average of 2 counts	0.707	0.155
^133Ba Blank #1	0.316	0.094
^133Ba Blank #2	0.305	0.089
^133Ba Blank #3	0.576	0.089
^133Ba Blank #4	0.419	0.132
^133Ba Blank #5	0.122	0.131
Average of ^133Ba Blanks	0.348	0.167^1

¹This is the standard deviation of the count rate of the ¹³³Ba blanks.

A similar analysis of net count rates of the unsealed standards, after net count rates were corrected for chemical recovery of radium, was performed. The results of this are shown in Figure 10.

Figure 10 Recovery corrected combined net count rates of ²²⁸Ac decay lines at 911 and 969 keV of unsealed standards vs. activity of unsealed standards

The R² value of 1, and the low background count rate for these standards which were significantly lower in activity than the unsealed standards, shows the method is suitable for ²²⁸Ra determination for a variety of samples, and can achieve relatively low detection limits. The data also indicates the assumptions of equal chemical recovery of radium and barium, enabling chemical recovery determination with ¹³³Ba are accurate.

3.1.2 Chemical recovery comparison HPGe vs NaI

As a quality control check on chemical recovery determinations, a set of freshwater mussels (Ryan et al 2005) prepared by the BaSO₄ method (Medley et al 2005) was counted in both the NaI and HPGe gamma spectrometers calibrated for these geometries. Table 6 shows a comparison of chemical recovery determined via both of these systems.

Table 6 Chemical recovery data for a set of freshwater mussels using ¹³³Ba as a tracer and counted on HPGe and NaI gamma spectrometers.

Sample ID	Gamma spectrometry (HPGe)		For alpha spectrometry (using NaI)
	Recovery (%)	%RSD	Recovery (%)	%RSD
MI02025	68.5	0.3	68.0	1.0
MI02026	35.1	0.3	36.4	1.5
MI02027	38.8	0.2	40.3	1.4
MI03135	67.2	0.4	68.5	1.1
MI03137	102.4	0.6	104.0	1.0
MI03138	93.3	0.5	93.3	1.0
MI03139	65.9	0.4	68.4	1.1

These results show very good agreement between the results obtained for both methods. This indicates that in ²²⁶Ra activity determinations for very active samples, the HPGe spectrometer can be used after alpha counting to accurately determine chemical recovery without the interference of radon daughters encountered on the lower resolution NaI spectrometer.

3.1.3 Detection limits

Six unsealed standards were prepared for determining the MDL. Table 7 details net counts (which are normalised to a 1 day count so as to accurately reflect standard deviation for this counting period), chemical recovery and percent relative standard deviation (%RSD). Variations in chemical recovery and count time inversely affect the MDL.

Table 7 Detection limit determination data

Sample activity (Bq)	Normalised net counts	%RSD	Chemical recovery (%)
0.137	110	24.0	83
0.253	238	12.1	83
0.461	434	7.77	80
0.946	820	5.38	78
6.43	5999	1.39	82
18.3	15551	0.88	76

In this report, the MDL is assumed to be the point at which % relative standard deviation (RSD) is 30%. It must be noted %RSD takes into account uncertainty associated with counting statistics only. Counting statistics in this technique can reliably be assumed to account for over 90% of total uncertainty (except for samples very close to detection limits, De Regge & Fajgelj 1999, Currie 1998).

The net count rate of the standards in both peaks combined versus %RSD was charted to determine the normalised net counts at 30% RSD in order to back calculate the MDL, this is shown in Figure 11.

Figure 11 Combined normalised net counts of ²²⁸Ac 911 and 969 keV peaks vs. %RSD for 6 unsealed standards

A MDL was determined to be 70 mBq by:

• 
  back calculating net count rates using the equation determined in Figure 11 assuming %RSD is 30%
  
• 
  back calculating ²²⁸Ra activity using Equation 7.
  
• 
  making the following assumptions:
  

85% chemical recovery of analyte

1 day (86.4 ks) count time

2.70% combined efficiency for 911 and 969 keV peaks

Stable, repeatable geometry of samples

The standard adopted for calculating detection limits by IUPAC and other organizations (ISO 1993) is based on Currie (1968), and gives the general equations detailed below (Table 8) for calculating the critical value (IDL), the Minimum Detectable Value (MDL) and the limit of quantification, or overall detection limit.

Using the standard deviation of the ¹³³Ba blanks shown in Table 5 and the formula in Table 8 and assuming we have a well-known blank to calculate the net count rate in the combined 911 and 969 keV peaks and dividing by the calculated efficiency of 2.70% for these peaks, we can calculate an IDL of 10 mBq, a MDL of 20 mBq and an overall detection limit of 62 mBq. This is quite similar to the detection limit of 70 mBq calculated using 30% RSD as the cut-off point.

Table 8 General formulae for calculating various detection limits, taken from Currie (1968). б_B is the standard deviation of the net count rate of the blank.

Limit type/type of measurement	Critical Value (IDL)	Limit of Detection (MDL)	Limit of quantification
Paired observations	2.33 x бB	4.65 x бB	14.1 x бB
‘Well-known’ blank	1.64 x бB	3.29 x бB	10.0 x бB

The flat nature of the sources prepared for radium determination gave a higher counting efficiency at the high energy gamma lines of ²²⁸Ac than expected. 2.70% efficiency for this technique compares with efficiencies of 1.03% for the large geometry and 1.59% for the small geometry for a standard pressed geometry method (pers. comm. Andreas Bollhoefer). This high efficiency is primarily responsible for the relatively low MDL of 70 mBq.

As counting statistics follow a normal distribution, uncertainty will decrease proportionally to the inverse square of the count time, so a fourfold increase in count time will half the uncertainty and approximately halve the MDL.

3.2 Alpha spectrometry method calibration

3.2.1 ²²⁸Ra determination with alpha spectrometry

The unsealed standards prepared were allowed an ingrowth period until ²²⁸Th activities were high enough for alpha spectrometric determination. Separation of thorium was performed using the methods developed in this project, and counted via alpha spectrometry.

Figure 12 shows the results obtained for ²²⁸Ra activity of the unsealed standards after back calculation from the determined ²²⁸Th activity at the time of thorium separation.

The measured versus expected activity shows an R² of 1 and a slope of nearly 1, indicating 100% recovery and good accuracy over a wide range of standard activities. Additional quality control for assessing recovery of the digestion process was performed indirectly through measurement of the ¹³³Ba recovery in the digest solution.

BaSO₄ is less soluble than ThSO₄ and therefore 100% recovery for ¹³³Ba is considered indicative of 100% recovery for thorium (Chaudhary et al 2006, Kirby 1964, Hyde 1960). Three polypropylene ¹³³Ba blank discs were digested by the method developed for this project, filtered through 0.45 µm into a plastic bottle and count rates from a NaI spectrometer in a selected region of interest were compared. Overall recovery was determined by methods described in Medley et al (2005) and is shown in Table 9. Recovery was essentially shown to be 100%, within uncertainty.

Figure 12 Measured vs actual ²²⁸Ra activity in unsealed standards as determined by ingrowth of ²²⁸Ra and measurement via alpha spectrometry

Table 9 ¹³³Ba chemical recovery for 3 standards after charring with concentrated sulphuric acid, digestion with concentrated hot nitric acid and hydrogen peroxide, then filtered through 0.45 µm. Methods used for gamma spectrometric (NaI) analysis are described in Medley et al (2005).

Standard identification number	^133Ba Standard 1	^133Ba Standard 2	^133Ba Standard 3
Chemical recovery and uncertainty in % (based on counting statistics only)	99±4.7	101±5.2	102±5.8

3.2.2 Detection limits

A detection limit of 5 mBq for the ingrowth method was calculated using Equation 11, and based on the following assumptions:

• 
  85% recovery for both the ²²⁸Ra and ²²⁸Th separation steps
  
• 
  A 12 month ingrowth period
  
• 
  A detection limit of 1 mBq for the alpha spectrometric determination of ²²⁸Th (Martin & Hancock 2004b, this is based on Currie 1968).
  

Detection limit determination for ²²⁸Ra via ingrowth of ²²⁸Th. Equation 10

Where –

A_Ra – Initial activity of ²²⁸Ra

R_Ra– Sample Recovery from radium separation

R_Th – Recovery calculated from thorium separation

t – The count time in kiloseconds (ks)

A_Th – The ²²⁸Th activity concentration at the date of initial thorium separation.

λ_Th – The decay constant of ²²⁸Th

λ_Ra – The decay constant of ²²⁸Ra

Very low backgrounds in alpha detector systems and from laboratory equipment, as well as the 100% efficiency demonstrated for the chemical recovery of the polypropylene source filter digestion, help to give the low detection limits of 5 mBq after 12 months ingrowth for this technique. The wide range of activities used for the unsealed standards also demonstrates that this method is suitable across a broad range of potential activities found in samples.