Standard addition

Anna-Lisa Hauswaldt1, Olaf Rienitz1, Reinhard Jährling1,

Nicholas Fischer2, Detlef Schiel1, Guillaume Labarraque2, Bertil Magnusson3

1 Physikalisch-Technische Bundesanstalt, Germany

2 Laboratoire National de Métrologie et d’Essais, France

3 Sveriges Tekniska Forskningsinstitut, Sweden

28th CITAC Members’ Meeting, 14th April 2013, Paris

Agenda

I. principle of standard addition

II. volumetric or gravimetric sample preparation

III. including the mass fraction of the standard into the

model equation

IV. using an internal standard

V. using a natural internal standard

1

I) Example: Rh in automobile catalysts

One-point calibration: w = 450 mg/g

Standard addition: w = 235.4 mg/g, u(y) = 5.8 mg/g

CCQM-P63:

2

180

200

220

240

260

280

300

w(R

h)

/ (m

g/g

)

Sample x

wx = ?

Standard z

wz known

I) Principle of standard addition

Step 1:

Sample

preparation

Step 2:

Measurement

Step 3:

Evaluation

~ wx measurand 3

wx wz

II) Volumetric vs gravimetric preparation

vs

4

Volumetric preparation – common practise

DIN 32633: 1998-12: Chemische Analytik – Verfahren der

Standardaddition Verfahren, Auswertung.

Harris, D.C.: Quantitative chemical analysis. New York: W.H.

Freeman and Company 1998.

II) Volumetric vs gravimetric preparation

Standard addition

Gravimetric

(DIN 32633:2013-05)

Volumetric

(DIN 32633:1998-12)

01 axay

ii

iii

m

mAy

1

,x

ii Ay V

Vx

i

i

z,z

i

i

im

mx

,x

,z

x1

0x

m

V

a

aw

z

1

0x w

a

aw

Disadvantages/problems of the old (volumetric) evaluation:

• Sample mass mx or sample volume Vx ‘exactly’ equal in all

measurement solutions

• Volume V ‘exactly’ equal in all measurement solutions

• Dependent on temperature

5

II) Volumetric vs gravimetric preparation

Therefore, in 2006 the gravimetric approach was proposed

Rienitz, O., Röhker, K., Schiel, D., Han, J., Oeter, D.: New Equation for

the Evaluation of Standard Addition Experiments Applied to Ion

Chromatography. Microchimica Acta 154 (2006) 21-25.

The new approach is now included in the German standard

DIN 32633: 2013-05: Chemische Analytik – Verfahren der

Standardaddition – Verfahren, Auswertung.

vs

6

Standard z

mz,i

wz

Solvent

II) Step 1: Gravimetric preparation

Sample x

wx

mx,i

Mass mi of

solution i with

density i

7

II) Step 2: Measurement yields signal Ai

A3 A2

A1

A4 A5

8

II) Step 3: Evaluation

A3 A2 A1

A4 A5

0 0 a0 y-intercept

tan a = a1 slope

wx / wz x ~ mz,i

a

y = a0 + a1 ∙ x

linear regression

y ~

Ai

Measurand 9

NEW

10

i

i

ii

ii

m

mwawa

m

mA

x,

z,

z1x1

x,

1

II) Step 3: Evaluation

Linear equation:

ii xaay 10

11

i

i

ii

ii

m

mwawa

m

mA

x,

z,

z1x1

x,

1

III) Including wz

Linear equation:

ii xaay 10

Model equation:

z

1

0x w

a

aw

,10 xaya

n

i

i

n

i

ii

xx

xxyy

a

1

2

11

OLS

Including wz in the equation for a1, assuming

Serapinas, P., Labarraque, G., Charlet, P., Ežerinskis, Ž., Juzikiene, V.:

Method of standard additions for arsenic measurements in water by ICP

sector field mass spectrometry at an accuracy comparable to isotope

dilution. J. Anal. At. Spectrom. 25 (2010) 624-630.

0),( 10 aau

12

i

i

ii

ii

m

mwawa

m

mA

x,

z,

z1x1

x,

1

III) Including wz

Linear equation:

ii xaay 10

Model equation:

z

1

0x w

a

aw

,10 xaya

n

i

i

n

i

ii

xx

xxyy

a

1

2

11

OLS

New model equation and measurement uncertainty with

Hauswaldt, A.-L., et al..: Uncertainty of standard addition experiments: a

novel approach to include the uncertainty associated with the standard in

the model equation. Accred. Qual. Assur. 17 (2012) No. 2, 129-138.

0),( 10 aau

13

III) Measurement uncertainty

Propagation of variances: z

1

0x w

a

aw GUM

2

and1

with1

1

2

102

1

1

2

2

z

x

2

0

2

z

2

relx

2

rel

n

xaay

s

xn

x

xx

xw

w

na

swuwu

n

i

ii

xy

n

i

in

i

i

xy

New: standard wz is included

Rh-example:

Aim: reducing the measurement uncertainty

%.13)(org/g28)(,g/g216 xrelxx wuwuw mm

Y

X

i

ii

A

AR

IV) Internal standard: motivation

200000

210000

220000

230000

t

I / (1

/s)

200000

210000

220000

230000

I / (1

/s)

t200000

210000

220000

230000

I / (1

/s)

t0,85

0,90

0,95

1,00

1,05

1,10

R

Signal analyte

s = 3,32 %

Signal internal standard

s = 3,37 %

Ratio of both

signals

s = 0,33 %

14

Standard z

mz,i

wz

solvent Sample x

wx

mx,i

Internal

standard y

my,i

wy

IV) Internal standard: sample preparation

15

IV) Internal standard: Ratios Ri

R3

A2 A1

A4 A5

0 0 a0

tan a = a1

wx / wz x ~ mz,i

a

y = a0 + a1 ∙ x

y ~

Ri

A3

R4 R5

R2 R1

16

17

i

i

i

i

im

mwawa

m

mR

x,

z,

z1x1

x,

y,

IV) Internal standard: equations

Linear equation:

ii xaay 10

Model equation:

z

1

0x w

a

aw

Measurement uncertainty:

n

i

i

xy

xx

xw

w

na

swuwu

1

2

2

z

x

20

2

z2

x2 1

relrel

GUM

Y

Xwherebut

1not and

with

x,

y,

x,

x,

z,

i

ii

i

i

ii

ii

iii

i

i

i

A

AR

m

mRy

m

mAy

m

mx

Standard addition with an internal standard

18

i

i

i

i

im

mwawa

m

mR

x,

z,

z1x1

x,

y,

IV) Internal standard: equations

Linear equation:

ii xaay 10

Model equation:

z

1

0x w

a

aw

Measurement uncertainty:

n

i

i

xy

xx

xw

w

na

swuwu

1

2

2

z

x

20

2

z2

x2 1

relrel

GUM

Y

Xwherebut

1not and

with

x,

y,

x,

x,

z,

i

ii

i

i

ii

ii

iii

i

i

i

A

AR

m

mRy

m

mAy

m

mx

Standard addition with an internal standard

A B C D A B C D

180

200

220

240

450

w(R

h)

/ (µ

g/g

)

Scenario

19

IV) Rh-Example: results

Intermediate result wx Final result w

Rienitz, O.: Uncertainty of standard addition experiments using an internal standard

and gravimetric preparation – determination of Rh in automobile catalysts. In:

Tagungsbericht 4. VDI Fachtagung Messunsicherheit praxisgerecht bestimmen,

12./13.11.2008, Erfurt. Düsseldorf: VDI Verlag 2008, ISBN 978-3-98-12624-1-4.

A) One-point calibration

Standard addition:

B) gravimetric

C) gravimetric, with internal standard

D) as C) but with a multi-collector

(MC-ICP-MS)

CCQM-P63 reference value

median with MADE

20

Key comparison

CCQM-K89

Measurand:

Arsenic-mass fraction

internal standard:

Gallium (69Ga)

Yttrium (89Y)

Indium (115In)

V) Example: Arsenic in Herba Ecliptae

Ga Y In K89 Nat Ga Nat Y

1,1

1,2

1,3

1,4

1,5

1,6

1,7

w(A

s) /

(m

g/g

)

natürlicher ISinnerer StandardInternal standard natural

internal

standard

w(A

s) /

(m

g/g

)

21

Key comparison

CCQM-K89

Measurand:

Arsenic-mass fraction

internal standard:

Gallium (69Ga)

Yttrium (89Y)

Indium (115In)

V) Example: Arsenic in Herba Ecliptae

Ga Y In K89 Nat Ga Nat Y

1,1

1,2

1,3

1,4

1,5

1,6

1,7

w(A

s) /

(m

g/g

)

natürlicher ISinnerer StandardInternal standard natural

internal

standard

w(A

s) /

(m

g/g

)

V) Natural IS: sample preparation

Standard z

mz,i

wz

Solvent Sample x

wx

mx,i my,i

wy

Internal

standard y

Sample x and

Internal standard y

wy wx

mx,i

= my,i

22

V) Natural IS: measurement and evaluation

R3

0 0 a0

tan a = a1

wx / wz x ~ mz,i

a

y = a0 + a1 ∙ x

y ~

Ri

R4 R5

R2 R1

23

24

z,

1 x 1 z

x,

i

i

i

mR a w a w

m

V) Overview

Linear equation:

ii xaay 10

Model equation:

z

1

0x w

a

aw

Measurement uncertainty:

n

i

i

xy

xx

xw

w

na

swuwu

1

2

2

z

x

20

2

z2

x2 1

relrel

GUM

andwithx,

z,

i

i

im

mx

iR

without IS with IS natural IS

ii

ii

m

mA

1

x,

i

i

im

mR

x,

y,iy ii mm y,x,

as

25

Natural internal standard

published in:

V) Publications

Hauswaldt, A.-L., Rienitz, O., Jährling, R.: Standard addition with gravimetric

preparation and internal standard – including the uncertainty associated with the

internal standard – Derivation of a new model equation and use of a natural internal

standard. 135-144, in: Tagungsbericht 5. VDI Fachtagung Messunsicherheit

praxisgerecht bestimmen, 8./9.11.2011, Erfurt. Düsseldorf: VDI Verlag 2011, ISBN 978-

3-18-092149-5.

Rienitz, O., Jährling, R., Hauswaldt, A.-L.: Standard addition challenge. Analytical and

Bioanalytical Chemistry, (2012) 403:2461-2462.

Hauswaldt, A.-L.: Evaluation of measurement data in analytical chemistry. PTB-Bericht

CP-7. Bremerhaven: nw-Verlag 2013, ISBN 978-3-86918-308-4. (Dissertation)

DIN 32633: 2013-05: Chemische Analytik – Verfahren der Standardaddition – Verfahren,

Auswertung.

Summary

26

• standard addition: elaborative and accurate

• exact model

• one straightforward equation for MU

• gravimetric sample preparation better than volumetric (2006)

• mass fraction wz of the added standard z is included in

the model equation (2012)

• internal standard considerably reduces the MU (2008)

• natural internal standard (2013)

• experiment (practical) mathematics (abstract measurement)

NEW

NEW

Acknowledgements

Dr. Olaf Rienitz, Dr. Reinhard Jährling, Carola Pape,

all CITAC members for the great honor to get

the CITAC Best Papers Award 2012

Thank you for your attention!

The research within this EURAMET joint research project receives funding from the European

Community's Seventh Framework Programme, ERANET Plus, under Grant Agreement No. 217257.

Some slides are basing on my lecture at 08.11.2011 in Erfurt, during the 5th VDI Fachtagung

„Messunsicherheit praxisgerecht bestimmen“.

27

28

Bibliography 1

[1] Rienitz, O., Röhker, K., Schiel, D., Han, J., Oeter, D.: New Equation for the

Evaluation of Standard Addition Experiments Applied to Ion Chromatography.

Microchim Acta 154, 2006, 21-25

[2] Rienitz, O.: Uncertainty of standard addition experiments using an internal standard

and gravimetric preparation – determination of Rh in automobile catalysts.

Tagungsbericht 4. VDI Fachtagung „Messunsicherheit praxisgerecht bestimmen“, VDI

Wissensforum, 2008

[3] Hauswaldt, A.-L., Rienitz, O., Jährling, R., Fischer, N., Schiel, D., Labarraque, G.,

Magnusson, B.: Uncertainty of standard addition experiments: a novel approach to in-

clude the uncertainty associated with the standard in the model equation. Accred Qual

Assur 17, 2012, Nr. 2, 129-138

[4] Hauswaldt, A.-L., Rienitz, O., Jährling, R.: Standard addition with gravimetric

preparation and internal standard – including the uncertainty associated with the

internal standard – Derivation of a new model equation and use of a natural internal

standard. 135-144, in: Tagungsbericht 5. VDI Fachtagung Messunsicherheit

praxisgerecht bestimmen, 8./9.11.2011, Erfurt. Düsseldorf: VDI Verlag 2011, ISBN 978-

3-18-092149-5.

29

Bibliography 2

[5] Rienitz, O., Jährling, R., Hauswaldt, A.-L.: Standard addition challenge. Analytical

and Bioanalytical Chemistry, (2012) 403:2461-2462.

[6] Hauswaldt, A.-L.: Evaluation of measurement data in analytical chemistry. PTB-

Bericht CP-7. Bremerhaven: nw-Verlag 2013, ISBN 978-3-86918-308-4 (Dissertation).

Guides

[GUM] Evaluation of measurement data – Guide to the Expression of Uncertainty in

Measurement, JCGM 100:2008

[VIM] International vocabulary of metrology VIM – Basic and general concepts and

associated terms, JCGM 200:2008

[DIN] DIN 32633-1, Chemische Analytik – Verfahren der Standardaddition – Verfahren,

Auswertung, 2013

30

III) Derivation of the linear equation

i

i

i

ii

ii

ii

m

mwawa

m

wmwma

m

mA

x,

z,

z1x1

x,

zz,xx,

1

x,

1

ionconcentrat y sensitivit 1 ii aA

analyte theoffraction mass density with iii w

i

ii

im

wmwmw

zz,xx, and

i

ii

iiiim

wmwmawaA

zz,xx,

11

ixaa 10iy

31

III) Rh-example: measurement result

mimzmxxexp

dry

1 wf

ww

Then: complete budget for the measurement uncertainty

Model equation:

Aim: reducing the measurement uncertainty

with dry mass correction, uncertainty contributions resulting from

sample preparation and from the masses of sample, standard and

solvent

%.13)(org/g28)(,g/g216 xrelxx wuwuw mm

g/g29)(,g/g218 mm wuw

B C D

0

20

40

60

80

100 mi, m

z,i

wx

mx

fexp

Rel

ativ

e co

ntr

ibuti

on t

o u

nce

rtai

nty

/ %

Scenario

32

III) Beispiel: Rhodium

Relative Unsicherheitsbeiträge für die Szenarien B – D

33

I) Messunsicherheitsberechnung

2

11 1

210

2

1

1

2

2

z

x

20

2

z2

x2

n

xaay

sxn

x

xx

xw

w

na

swuwu

n

i

ii

xy

n

i

in

i

i

xyundmitrelrel

2 2 2GUM

2 2 2 2x x xx 0 1 z

0 1 z

x x x x x x0 1 0 z 1 z

0 1 0 z 1 z0 0

2

2x xz

z

( )

2 , 2 , 2 ,

w w wu w u a u a u w

a a w

w w w w w wu a a u a w u a w

a a a w a w

w wu w

w a

22

2 2x x x1 0 1 0

1 0 1 0

partialderi- 2 2 2vatives

2 2 20 z 0 z 0z zz 1 0 1 02 2

1 1 1 1 1

22 2

2 20x zz2 2

z 1 1

2 ,

2 ,

w w wu a u a a u a

a a a

a w a w aw wu w u a u a a u a

a a a a a

aw wu w u

w a a

20

1 0 1 0

1

2 , .a

a u a a u aa

Modellgleichung:

z

1

0x w

a

aw

partielle

Ableitungen

n

i

i

xy

n

i

i

xy

n

i

i

n

i

ixy

xx

xsaau

xx

sau

xx

xn

s

au

1

2

2

10

1

2

2

12

1

2

1

22

02 ,

1

,,

Aus den Unsicher-

heiten des OLS-

Algorithmus folgt

die relative MU:

34

III) Beispiel: Arsen in Herba Ecliptae

Gallium

Arsen

Yttrium

Indium

Relative Isotopic Abundance Table