1833-46

Workshop on Understanding and Evaluating RadioanalyticalMeasurement Uncertainty

Gyula KIS-BENEDEK

5 - 16 November 2007

International Atomic Energy Agency IAEAAgency's Laboratories SeibersdorfChemistry Unit, A-2444 Seibersdorf

AUSTRIA

Uncertainty in gas proportional counting.

Counting Uncertainty in Using Gas Proportional Counters

Main Types of Proportional Counters

1. Gas Flow Proportional - with window (laboratory alpha-beta counters)- windowless

2. Air Proportional (alpha counting only)

3. Sealed proportional (e.g., BF3, 3He neutron detectors)

Applications

• Gross alpha and or beta counting- Filter- Smear (wipe test) - Water (residue)- Soil,

• Sources from separated alpha or beta emitting radionuclides- Sr-90, Y-90 or C-14

Basic Detector Theory

+ Anode wire

_Kathode

Electron avalanche

Incident radiation

Detector gas volume

Primary ionisationAr →Ar+ +e-

Gas proportional detectors

Basic Detector Theory

• Gain• Number of electrons reaching the anode wire

~ U (applied detector voltage bias)

• number of electrons produced by the particle~ Energy of the particle/Eigas

nNGain =

Basic Detector Theory

Beta background

Alpha background

Chi Square test for variances – equipment performance

Expected counting uncertainty :

Calculated standard deviationof n counting:

Chi square:

Hypothesis:Degree of freedom: n-1

N Nσ =

2 2* ( )

*( 1)

n n

i ii i

N

n N Ns

n n

−=

−

∑ ∑

22

2 *( 1)N

N

S nχσ

= −

0 1: ; : <N N N NH s H sσ σ=

Sources

• Thick source – infinite thickness, saturation layer thicknessα: 0.02 gcm-2 , <3% efficiency, effect of humidity, structure of surface

• Fixed source size

• Variable source thickness Mass attenuation curve, Standard addition

Attenuation Curve

y = -0.064Ln(x) + 0.13R2 = 0.997

0.3500

0.3700

0.3900

0.4100

0.4300

0.4500

0.4700

0.4900

0.0000 0.0050 0.0100 0.0150 0.0200 0.0250

Surface density (Sr-oxalate g/cm2)

Sr-9

0 +

Y-90

Cou

ntin

g Ef

ficie

ncy

Efficiency – beta energy

Determination of saturation layer thickness

1000.00

1500.00

2000.00

2500.00

3000.00

3500.00

4000.00

4500.00

1 2 3 4 5 6 7

K2SO4 gcm-2

beta CPM

Alpha attenuation curve

Alpha counting efficiency

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.005 0.01 0.015

NaCl gcm-2

Magnified picture of a 210Po / NaCl source

Calibration

*st Bg

st

I IA pβ

ε−

=

Depends on layer thickness, composition, source/sample distribution on plate

Saturation layer thickness: ( )st Bg

calm

I If

A−

=

mA Bq/g

Calculation of activity

*sample BG

source

i iA

pβε−

=

sample BGmsource

cal

i iA

f−

= Bq/g

Corrections

• Decay- Calibration source/tracer- Reporting result to a reference date

- Decay/ingrowth during counting

• Recovery

*

1/ 2

ln 2;toA A e

tλ λ− ∆= =

*

01* ;

*

ct

cc

ei it

λ

λ

−−=

Crosstalk Spillover

in

in in

iX

i iα β

α βα β α α

→ =+

in

in in

iX

i iβ α

β αβ α β β

→ =+

* *1c

i i X i Xi

X Xα α β α β β α

αβ α α β

→ →

→ →

− −=

− −* *

1c

i i X i Xi

X Xβ β α β α α β

ββ α α β

→ →

→ →

− −=

− −

40K

40K 40Ca

Eγ: 1460.8 keV(10.7%)

β−

EX

t1/2: 1.277E9 Y

EβMAX: 1.311 MeV(89.3%)

40Ar

Isotopic abundance: 0.000117Am: 30.9 Bq/g K

Calculation of uncertainties 1

Approach 1 The combined uncertainties were obtained from the components as using the

uuu 2

B

2

ABA+=

± ,

Bu

Auu 2

2

B2

2

AB*A

B*A += and Bu

Auu 2

2

B2

2

AA/B B

A+= and

uλutueu 2

t

22

λ

22t*λ

**AeA 0

t*λ0

++= , λ=ln2/t1/2, formulae, breaking the used to

formulae for calculation of the activity concentration to expressions covered by one of the ones above.

Calculation of uncertainties 2

Contribution, % : [(δε/δxi)2.uxi

2.100]/uε2

SF=(δ y / δxi), uy=ΣSFi^2*ui^2

Using the partial derivatives method

Analysis and evaluation of uncertainty sources:

Calculation of uncertainties 3• using the spreadsheet (Kragten) method

Quantulus CAL2-05/1Table 1 Spreadsheet Method for Uncertainty Calculation in the Efficiency. Calibration of Quantulus for the Determination of 210Pb

Parameter xi ts,CAL mvial mvial+carr.sol cPb mvial mvial+standard A0 210Pb fgravimetry mfilter

Unit min g g g/g g g - - gValue xi 60 14.9364 16.03654 0.0274 16.03672 17.1326 12.45 0.70185 0.03654

uxi 0 0.00010 0.00010 0.000020565 0.00010 0.00010 0.26 0.00041 0.00010Parameter xi

mvial 14.93635 14.93645 14.93635 14.93635 14.93635 14.93635 14.93635 14.93635 14.93635mvial+carr.sol 16.03654 16.03654 16.03664 16.03654 16.03654 16.03654 16.03654 16.03654 16.03654

cPb 0.0274 0.0274 0.0274 0.0274 0.0274 0.0274 0.0274 0.0274 0.0274mvial 16.03672 16.03672 16.03672 16.03672 16.03682 16.03672 16.03672 16.03672 16.03672

mvial+standard 17.13260 17.13260 17.13260 17.13260 17.13260 17.13270 17.13260 17.13260 17.13260A0 210Pb 12.4500 12.4500 12.4500 12.4500 12.4500 12.4500 12.7100 12.4500 12.4500fgravimetry 0.70185 0.70185 0.70185 0.70185 0.70185 0.70185 0.70185 0.70226 0.70185

mfilter 0.03654 0.03654 0.03654 0.03654 0.03654 0.03654 0.03654 0.03654 0.03664mfilter+Pb(C2O4) 0.07377 0.07377 0.07377 0.07377 0.07377 0.07377 0.07377 0.07377 0.07377

IACAL 349.654 349.654 349.654 349.654 349.654 349.654 349.654 349.654 349.654IABG 1.772 1.772 1.772 1.772 1.772 1.772 1.772 1.772 1.772IBCAL 24.957 24.957 24.957 24.957 24.957 24.957 24.957 24.957 24.957IBBG 0.703 0.703 0.703 0.703 0.703 0.703 0.703 0.703 0.703fA/B 1.049 1.049 1.049 1.049 1.049 1.049 1.049 1.049 1.049t 391564800 391564800 391564800 391564800 391564800 391564800 391564800 391564800 391564800

λ 210Pb 9.85E-10 9.85E-10 9.85E-10 9.85E-10 9.85E-10 9.85E-10 9.85E-10 9.85E-10 9.85E-10

εPb-210 0.669 0.669 0.669 0.669 0.669 0.669 0.655 0.668 0.671uε Kragten 0.01511

uε parc. Der. 0.01537εi,Pb - εPb -6.078E-05 6.078E-05 5.016E-04 6.103E-05 -6.102E-05 -1.368E-02 -3.904E-04 1.801E-03

Σ (ε i,Pb - εPb)2 2.283E-04 (ε i,Pb - εPb)2 3.695E-09 3.695E-09 2.516E-07 3.725E-09 3.723E-09 1.871E-04 1.524E-07 3.244E-06uε/ε, % 2.26 (ε i,Pb - εPb)2

3.69E-09 3.69E-09 2.52E-07 3.72E-09 3.72E-09 1.95E-04 1.53E-07 3.23E-06

SF by Kragten δε/δxi -0.6078 0.6078 24.3888 0.6103 -0.6102 -0.0526 -0.9523 18.0108

SF by Parc. Deriv. δε/δxi -0.608 -0.608 24.389 0.610 -0.6102 -0.0537 -0.9528 17.96244

Contribution, % Kragten 1.62E-03 1.62E-03 0.11 1.63E-03 1.63E-03 81.96 0.07 1.42Contribution, % parc. Der. 1.56E-03 1.56E-03 0.11 1.58E-03 1.58E-03 82.57 0.06 1.37

Contribution, % = [(δε/δxi)2.uxi

2.100]/uε2