Std Add mit nat IS - CITAC€¦ · 28 th CITAC Members’ Meeting, 14 April 2013, Paris . Agenda I....
Transcript of Std Add mit nat IS - CITAC€¦ · 28 th CITAC Members’ Meeting, 14 April 2013, Paris . Agenda I....
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 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
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: