Detection Limits

N no longer >> NB at low concentration

What value of N-NB can be measured with statistical significance?

Liebhafsky limit:

Element is present if counts exceed 3X precision of background:

N > 3(NB)1/2

Ziebold approximation:

CDL > 3.29a / [(nτP)(P/B)]1/2

τ = measurement time

n = # of repetitions of each measurement

P = pure element count rate

B = background count rate (on pure element standard)

a = relates composition to intensity

Or 3.29 (wt.%) / IP[(τ i) / IB]1/2

IP = peak intensity

IB = background intensity

τ = acquisition time

i = current

Ave Z = 79

Ave Z = 14

Ave Z = 14, 4X counts as b

Where

Detection limit (Ancey)

α : Risk of considering that C>0 when it is in fact C=0β : Risk of considering that C=0 when it is in fact C>0

By default, we will use α = β = 5%.

0

10

20

30

40

50

60

70

80

90

100

0 100000 200000 300000 400000 500000

current * time (nA - sec)

pp

m

Detection limit for Pb

PbMα measured on VLPET

200nA, 800 sec

Can increase current and / or count time to come up with low detection limits and relatively high precision

But is it right?

Accuracy

All results are approximations

Many factors

Level 1

quality and characterization of standards

precision

matrix corrections

mass absorption coefficients

ionization potentials

backscatter coefficients

ionization cross sections

dead time estimation and implementation

Evaluate by cross checking standards of known composition (secondary standards)

Level 2 – the sample

Inhomogeneous excitation volume

Background estimation

Peak positional shift

Peak shape change

Polarization in anisotropic crystalline solids

Changes in Φ(ρZ) shape with time

Measurement of time

Time-integral effects

Measurement of current, including linearityis a nanoamp a nanoamp? Depends on measurement

– all measurements include errors!

Time-integral acquisition effects

drift in electron optics, measurement circuitry

dynamic X-ray production

non-steady state absorbed current / charge response in insulating materialsbeam damagecompositional and charge distribution changessurface contamination

Overall accuracy is the combined effect of all sources of variance….

σT2 = σC

2+σI2+σO

2+σS2+σM

2

σT = total error

σC = counting error

σI = instrumental error

σO = operational error

σS = specimen error

σM = miscellaneous error

Each of which can consist of a number of other summed terms

Becomes more critical for more sensitive analyses - trace element analysis

Sources of measurement error –

Time-integral measurements and sample effects

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Time (min)

Cp

s/n

A

2σ counting statistics

0 5 10 15 20 25 30

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

54000 55000 56000 57000 58000 59000 60000 61000 62000 63000 64000

Cp

s/n

A

Wavelength (sinθ)

130

131

132

133

134

135

136

137

138

0 500 1000 1500 2000 2500 3000 3500

time (sec)

ab

s. c

urr

en

t (n

A)

130

131

132

133

134

135

136

137

138

0 500 1000 1500 2000 2500 3000 3500

time (sec)

ab

s. c

urr

en

t (n

A)

130

131

132

133

134

135

136

137

138

0 500 1000 1500 2000 2500 3000 3500

time (sec)

ab

s. c

urr

en

t (n

A)

ideal

Beam damage

Monazite

LGG246-5 Lower Granite Gorge - Grand Canyon

15kV, 200nA, 30 min

Sources of measurement error:

Current and dead-time

SP2 1-12-04After picommeter adjustment

0.97

0.98

0.99

1

1.01

1.02

0 50 100 150 200 250 300

current (nA)

I /

I 15

Initial

Initial

After adjustment

After adjustment

Sources of measurement error:

Extracting accurate intensities – peak and background measurements

Background shape depends on

Bremsstrahlung emission

Spectrometer efficiency

PHA effects relating to trace analysis

LaPO4 and monazite

0.0

2.0

4.0

6.0

8.0

10.0

12.0

1 2 3 4 5 6

Pressure (bars)

La

La

1 (

2) /

Au

LaPO4

Low Th monazite

Detector gas type and pressure

GdPO4 Pb region (PET)sp3

y = 8.520777E+01e -7.237583E-05x

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6

1.7

54000 56000 58000 60000 62000 64000

wavelength (sin-theta)

inte

ns

ity

(c

ps

/nA

)

VLPET

Expon. (VLPET)

Linear (Series2)

PbMα

UMass sp3 GdPO4 and GSC 8153 (VLPET)

y = 8.520777E+01e-7.237583E-05x

0.80

0.90

1.00

1.10

1.20

1.30

1.40

1.50

1.60

1.70

54000 56000 58000 60000 62000 64000

wavelength (sin-theta)

inte

ns

ity

(c

ps

/nA

)

VLPET

Series2

Pb Ma

GSC 8153 mzt

Expon. (VLPET)

Linear (Series2)

PbMα

Pb Ma bkg (PET LGG 246-5 m1)

0.19

0.20

0.21

0.22

0.23

59000 59500 60000 60500 61000 61500

Wavelength (sin)

I (c

ps

/nA

)

PbMa

High Th Bkg.

Low Th Bkg.

7.3 wt% Th

4.0 wt% Th

exp. lin.

y = 0.679x-1

0

2

4

6

8

10

12

14

0.00 0.10 0.20 0.30 0.40 0.50 0.60

net intensity (cps/nA)

% e

rro

r o

f n

et in

ten

sity

Measured

Theoretical based on run5

At ~1000ppm Pb, 10% error can easily produce an age error of 35-40Ma (5 wt.% Th, 4000ppm U)

Becomes 50% error at ~ 0.015 net intensity

bkg net intensity (Pk-bkg)actual bkg 0.23544 0.059155lin fit 1 0.24223 0.052365diff 0.00679 -0.00679%error 2.883962 11.47832

bkg net intensity (Pk-bkg)actual bkg 0.23268 0.0956lin fit 1 0.2426 0.08568diff 0.00992 -0.00992%error 4.263366 10.37657

bkg net intensity (Pk-bkg)actual bkg 0.249807 0.131163lin fit 1 0.25831 0.12266diff 0.008503 -0.008503%error 3.403828 6.482773

bkg net intensity (Pk-bkg)actual bkg 0.29714 0.33756lin fit 1 0.30466 0.33004diff 0.00752 -0.00752%error 2.530794 2.227752

bkg net intensity (Pk-bkg)actual bkg 0.26367 0.21239lin fit 1 0.27187 0.20419diff 0.0082 -0.0082%error 3.109948 3.860822

Pb

0

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12000

14000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

net intensity (Pk-bkg cps/nA)

pp

m

Concentration (ppm)Y TH Pb U Age (Ma)

fitted Ave 19196 48043 1094 3984 400.2bkg. SStd 3518 3043 119 1343 8

StdErr 1573 1361 53 601 3.6

linear Ave 19194 48007 996 3958 365.4bkg. SStd 3519 3039 123 1340 10.1

StdErr 1574 1359 55 599 4.5

Sources of measurement error - Peak shifts

Wavelength may shift between standard and sample (or between samples) if X-ray transition involves valance electrons

Example: Y Lγ2,3

transitions from N2 (4p1/2) and N3 (4p3/2) levels

Critical in Pb measurement in monazite: PbMα - YLγ overlap

YPO4 (tetragonal) Monazite (monoclinic)

O coordination 8-fold 9-fold

Ave REE-O bond length (Å) 2.346 2.559

YPO4

Calculate peak wavelength shift of -4.5x10-3Å in monazite relative to YPO4

Results in overestimation of overlap:

36ppm Pb / wt.%Y