T102 Redetermination of the Avogadro constant … volume determination PTB‘s sphere interferometer with spherical symmetry PTB‘s sphere interferometer enables complete topographies

T&M Conference Johannesburg 07.10.2013(1)

"Redetermination of the Avogadro Constant for the new Definition of the mole and the kilogram”

Detlef Schiel, Bernd Güttler, Axel Pramann, Olaf RienitzPhysikalisch-Technische Bundesanstalt, 38116 Braunschweig, Germany


Speed of light

Definition of Si units by fundamental constants

Boltzmann-constant

Avogadro-constant

Luminous efficacy Planck- constant

Atomic transitions

Elementary charge

cd

K

s

kg

m

mol

A


Mass values of the prototypes in 1889, 1950 and 199 0

-100

-80

-60

-40

-20

0

20

40

60

80

100

1880 1900 1920 1940 1960 1980 2000

year

∆∆ ∆∆m/µ

gred: International Prototypegreen: BIPM, Official Copies

orange: no.25, BIPM , for special useblack: national prototypes

„Stability“ of the Kilogram Prototype

50 µg


Precondition for new defintion

Measurement challenge :

u(NA) or u(h) ≤ present situation

Three measurement results of NA or h availableone of them should have a rel. stand. uncertainty of 2· 10-8 andtwo should have a rel. standard uncertainty of 5· 10-8


International Avogadro Coordination (IAC)CCM Working Group on the Avogadro Constant (WGAC)

2010 Grenoble


Measurement of NA

N = VSphere/ VAtom

n = N / NA = m / M

NA = (M / m) (VSphere/ VAtom)

http://www.msm.cam.ac.uk/phase-trans/2003/MP1.crystals/MP1.crystals.html

3

sphere

A

8

am

VMN

⋅⋅⋅=


International Avogadro Coordination

Multicollector ICPMS

X-Ray Interferometer

Optical sphere interferometer

3sphere

sphere

A

8

am

VMN

⋅⋅⋅=

Mass comparator

Surface layer : XRR, XRF, XPS,opt. ellipsometry

Impurities: IR, NAA


Material for the NA measurement

Isotopically enriched Si(28) material


Interferometrical volume determination

camera 1 camera 2

mK-temperature stabilisation

diode laser

collimator

Fizeau-Objective 1

Fizeau-Objective 2

thousands of diameters are measured simultaneously


Interferometrical volume determination

PTB‘s sphere interferometer with spherical symmetry

PTB‘s sphere interferometer enables complete topographies of spheres, ndiameter ≈ 600 000.

The radius uncertainty is 0.7 nm or 8 ×10-9

Radius topography of 28Si-sphere S8. Peak to valley deviations from roundness amount to 99 nm.


This image cannot currently be displayed.This image cannot currently be displayed.

Combined optical and x-ray interferometry

1 cm

∆s

INRIM X-ray interferometer


Mass comparison in air and under vacuum on the 28Si sphere S5

87730

87740

87750

87760

87770

87780

87790

87800

87810

87820

87830

02/2008 06/2008 09/2008 12/2008 03/2009 07/2009 10/2009 01/2010 05/2010 08/2010date (Month/Year)

Mas

s (v

alue

-1kg

) (µ

g)

PTB air (hydrostatic department) NMIJ air (hydrostatic department)

NMIJ air (mass department) NMIJ vacuum

BIPM air BIPM vacuum

PTB air (mass department) PTB vacuum (mass department)

IAC vacuum (Weighted mean) IAC air (Weighted mean)

1.10-8

Values in air are corrected by the amount of water adsorbed

The error bars represent the combined uncertainty (k=1)

S5

ur(m): 4 ×10-9

Mass comparison


Oxid layer (PTB, NMIJ, METAS, BIPM)

X-ray reflectometry at BESSY II:Determination of layer thickness (absolute)

X-ray spectroscopy (METAS, BESSYII, PTB):Stoichometry, impurities, mass density

Spectral ellipsometry (PTB, NMIJ):Topography of layer thickness

Influences and Risks:

• Optical constants• Contamination• Surface quality

Total uncertainty: 0,3 nm14 µg


Determination of the molar mass of silicon

● three isotopes: 28Si, 29Si, 30Si● amount fractions x ↔ isotope ratios R● Challenge: Target uncertainty of uM,rel ≤ 1·10-8

( ) ( )[ ]∑=

⋅=30

28

SiSi)Si(i

ii MxM

( )∑=

=30

28

Si

jj

ii

R

Rx


92.2 %

4.7 %3.1 %

28Si 29Si 30Si

Measurement challenge I

nat. Si

R 28/28 1

R 29/28 5.0 · 10-2

R 30/28 3.4 · 10-2

Isotopic ratios

U < 10-7

Natural Si


Measurement challenge II

nat. Sienriched

Si-28

R 28/28 1 1

R 29/28 5.0 · 10-2 4.1 · 10-5

R 30/28 3.4 · 10-2 1,3 · 10-6

Isotopic ratios

U < 10-7 U ≈ 10-3

nat. Si

R 28/28 1

R 29/28 5.0 · 10-2

R 30/28 3.4 · 10-2

> 99.99 %

0.0041 %0.00013 %

28Si 29Si 30Si

„Si28“


New concept

w30+29 = wimp = =m29 + m30

m28+m29+m30

mimpm28+mimp

30S29Si

28Si

w 30+29� 29Si and 30Si treated like a virtual two-isotop-element impurity in the isotopically enriched Si (28) matrix

�Measurement of the mass fraction w30+29 by IDMS


Virtual Element IDMS

Metrologia 47 (2010) 460-463


Measurement procedure

Si (crystal)

alkaline dissolution

Si-solution

ID ICPMS-measurement

Isotopic composition of the sample

Molar Mass


Measurement technique

Multicollector-Inductively-Coupled-Plasma Mass Spectrometer (MC-ICP-MS)

28Si29Si 30Si

Sample

MagnetFaraday-Detectors

Neptune (Thermo-Finnigan)


Mass interference

High resolution scan of WASO17 and IDMS blend ("28- Si"/"30-Si")

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

28.945 28.950 28.955 28.960 28.965 28.970 28.975 28.980

M /(g/mol)

ion

sign

al/V

IDMS 29Si

WASO17 29Si

29Si

28SiH


PTB results (using NaOH)

27.9769690

27.9769692

27.9769694

27.9769696

27.9769698

27.9769700

27.9769702

27.9769704

27.9769706

27.9769708

27.9769710

4.4

5.B2.

1.4

5.B3.

1.1.

3

5.B4.

1.1.

4

7.1.

2.3

7.2.

4.5

8.A2.

1.4

8.B4.

1.1.

3

9.8

sample

M/(

g/m

ol)

urel = 8.2·10-9


27.9769680

27.9769685

27.9769690

27.9769695

27.9769700

27.9769705

27.9769710

PTB 2011 NRC 2012 NIST 2013 (S5) NIST 2013 (S8) PTB 2013

M/(

g/m

ol)

Current situation of results

urel = 6·10-9

Molar Mass of „Si28“

∆Mrel = 6.5·10-8

∆Mrel = 1.1·10-8

NaOH NaOH TMAH TMAH TMAH


NA = 6.022 140 84(18) · 1023 mol -1

Avogadro constant

Received from Si crystal experiment


Intended redefinition of mole and kilogram

• Definitions• Realizations• Consequences (?)


The amount of substance of a system which contains as many elementary entities1 as there are atoms in 0.012 kilogram of carbon (12).

Current definition of the mole

1Elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles

Indentification

NA is derived from the kghas to be measured and

has an uncertainty

12 g (12C) = 1 mol ( 12C){NA} atoms in 1 mol


Macroscopic level

Atomic level

NA NA

Current definition of the mole

Definitions: M(12C) = 12 g/molAr(12C) = 12

Furthermore: Mu = mu NA g/mol

M(A) = Ar(A) Mu g/mol

m(12C) mu

M(12C) Mu

Mu = 1 g/molu(Mu) = 0 g/molNA measured mol -1

u(NA) measured mol -1

m(A) = Ar(A) mu g/mol

Ar( 12C)M(A)

Ar(A)

Ar( 12C)m(A)

Ar(A)


Intended new definition of the kilogram

kg

h definedU(h) = 0

The kilogram, kg, is the SI unit of mass; its magnitude is set by fixing the numerical value of the Planck constant to be equal to exactly 6.626 068X ·10-34 when it is expressed in the unit s-1 m2

kg, which is equal to J s.

Foto: OkerlandarchivFoto: OkerlandarchivFoto: Okerlandarchiv


Intended new definition of the mole

mol kg

NA definedU(NA) = 0

h definedU(h) = 0

The mole, mol, is the unit of amount of substance of a specifiedelementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 141X·1023 when it isexpressed in the unit mol-1.


?


Intended new definition of the mole

mol kg

NA definedU(NA) = 0

h definedU(h) = 0

∞

=R

MecAhN ur

A 2

)( 2α

c light velocity, Ar(e) relative mass of the electron, Mu = (10-3 kg mol-1), α fine structure constant, R∞ Rydberg constant, e elementary charge

The mole, mol, is the unit of amount of substance of a specified elementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14129 *1023 when it is expressed in the unit mol-1.


The mole, mol, is the unit of amount of substance of a specifiedelementary entity, which may be an atom, molecule, ion, electron, any other particle or a specified group of such particles; its magnitude is set by fixing the numerical value of the Avogadro constant to be equal to exactly 6.022 14129 *1023 when it isexpressed in the unit mol-1.


After new definition of the mole

New definition: NA = 6.0221X·1023 g/molu(NA) = 0 g/mol

Therefore: Mu measuredu(Mu) ≈ 1.4 x 10-9 g/mol

2)(

2

αecA

RhNM

r

Au

∞=

Macroscopic level

Atomic levelAr( 12C)

Ar( 12C)

NA NA

M(A) = Ar(A) Mu g/mol

m(12C) mu

M(12C) Mu

m(A) = Ar(A) mu g/mol


Summary of the changes

After defintion• Number of entities in a mole is fixed (and equal to NA exactly)

• Molar masses are uncertain (u(Mu) = 1.4·10-9 )

At present• The mass scale fixed ( Mu is 1 g/mol exactly)

• Number of entities in a mole is an uncertain value (u(NA) = 3·10-8 )


Experiments for definition NA and h

● Counting atoms :

Determination of the Avogadro constant with silicon

crystal method,

Current value: urel(NA) = 3· 10-8

● Generating standard forces :

Determination of Planck constant with Watt balance

experiment,

Current value: urel(NA) ~ 6· 10-8


Present situation of NA results

6.022138

6.022139

6.022140

6.022141

6.022142

6.022143

6.022144

1990 1995 2000 2005 2010 2015

NA

in 1

023

mol

-1

Year of publication

NPL

NISTNIST

NPL

NPL

IAC

NRC

NISTpreliminaryMETAS


Possible realization by XRCD experiment

N / NA = n Is an absolute measurement of amountof substance without using weighing

Realization of the mole

1) VSphere/ Vatom = N N / NA = n

2) m / M = n

N / NA = m / M


Consequences for chemists

No Change

except that the relative uncertaintyof an amount of substance valuecannot be smaller than 1.4·10-9

Barry Taylor, Metrologia 46 (2009) L16-L19

n = m / M


Dissemination and uncertainty propagation

Reference standards ofE1accredited laboratoriesReference standards of

E1accredited laboratories

National standards of NMIsNational standards of NMIs

BIPM reference standardsBIPM reference standards

BIPM Working standardsBIPM Working standards

Secondary standards of NMIs and best standards according to CMCSecondary standards of NMIs and best standards according to CMC

Standards of customers of E1 accredited laboratories


0 µg

6 µg

14 µg

25 µg

≤ 83 µg (E1)

6 µg

Present system After redefinition

20 µg

44 µg

Ex. 1 (CCM req.)

30 µg

85 µg (E2)

Ex. 2

30 µg

71 µg

71 µg

77 µg

Best realisation of the kilogramBest realisation of the kilogram 50 µg

Ex. 3

42 µg

43 µg

32 µg

53 µg

≤ 83 µg (E1) 100 µg (E2)

30 µg

30 µg 43 µg

43 µg

71 µg

71 µg









0 µg

6 µg

14 µg

25 µg

≤ 83 µg (E1)

6 µg


20 µg

44 µg

Ex. 1 (CCM req.)

30 µg

85 µg (E2)

Ex. 2

30 µg

71 µg

71 µg

77 µg


Ex. 3

42 µg

43 µg

32 µg

53 µg

≤ 83 µg (E1) 100 µg (E2)

30 µg

30 µg 43 µg

43 µg

71 µg

71 µg

6 µg

6 µg

w


Acknowledgement

Molar mass measurements:

Olaf RienitzAxel Pramann Avogadro team leader:

Peter BeckerHorst Bettin


Thank youfor your attention!


XRCD experiment for link to the kg

N · M / NA = m abs. measurement of the mass of thesphere without weighing

M / NA = m(Si) absolute mass of a Si-atom

Realization of the link to the kg


2) m / M = n

N / NA = m / M


Realization (traceability chain)

Measurement Uncertainty

SIThe mol is that amount-of-substance

which contains as many entities as there are in 12 g 12C. [n] = 1 mol

Values

n (Cu, X)Amount of copper in XSample X

... Y)(Cu,

)X Cu,(=

n

n

Referencematerial Y

n (Cu, Y)Amount of copper in Y

...Z) (Cu,

) YCu,(=

n

n

Primary (national)standard Z

n (Cu, Z)Amount of copper in a material Z

=)ZCu,(nCu

pur M

*wm

Peter Becker: The Avogadro Project: a 25 Year Quest, 20 Mai 2011, NIST


Traceability system for elemental analysis in Germany

Matschat, R., Kipphardt, H., Rienitz, O., Schiel, D., Gernand, W., Oeter D.: Accreditation and Quality Assurance, 10 (2006), S. 633-639

Dissolution

Precision measurementCertification of

commercial solutions

Primary elemental standards Primary elemental solutions

Commercial solutions Transfer solutions


m(Cu) = n(Cu)·M(Cu) m(Si) = n(Si)·M(Si)

n(Cu) = n(Si) · Ar(Si))/Ar(Cu) or

N(Cu) = N(Si) · Ar(Si))/Ar(Cu)

„Idea“ for link on primary level


XRCD experiment after the new defintion

N = VSphere/ VAtom

n = N / NA = m / M

m / N = m(Si) absolute mass of a Si-atom

M (Si) molar mass (isotope composition)

Remeasurement of the molar mass unitallows to verify e.g. if the mass of a mol 12C is still 12g


O. Rienitz, A. Pramann, D. Schiel: Novel concept for the mass spectrometric determination of absolute isotopicabundances with improved measurement uncertainty: Part 1 – theoreticalderivation and feasibility study, Int. J. Mass Spectrom. 289 (2010) 47

G. Mana, O. Rienitz:The calibration of Si isotope ratio measurements, Int. J. Mass Spectrom. 291 (2010) 55.

A. Pramann, O. Rienitz, D. Schiel, B. Güttler: Novel concept for the mass spectrometric determination of absolute isotopicabundances with improved measurement uncertainty: Part 2 – Development of an experimental procedure for the determination of the molar mass of silicon usingMC−ICP−MS, Int. J. Mass Spectrom. 299 (2011) 78.

A. Pramann, O. Rienitz, D. Schiel, B. Güttler, S. Valkiers: Novel concept for the mass spectrometric determination of absolute isotopicabundances with improved measurement uncertainty: Part 3 – Absolute molar massof silicon highly enriched in 28Si, Int. J. Mass Spectrom. 305 (2011) 58.

Literature


Traceability system for elemental analysis

Measurement of the test laboratory

Precison measurement for the certification

Precision measurement of the element content

Purity determination

Gravimetrical preparation of the primary solution

sample X

Sample solution wX(E)

Secundary standard Y

Commercial sol., Urel= 0,3% wY(E)

Transferstandard T

Transfer solution, Urel= 0,1% wT(E)

SI

kg and mol NA

Primary standard

Primary solution, Urel= 0,05% wS(E)

Pure material, Urel= 0,01% wpur

diss

emin

atio

n


Isotopic composition of SiF 4 by Gas-MS

FaradaydetectorsFaradaydetectors

AmplifierhousingAmplifierhousing

MagnetMagnet

Ion sourceIon source

Faradaydetectors

Amplifierhousing

Magnet

Ion source

MAT 253MC-IRMS


Preparation of SiF 4 - reference gases

42 SiFF 2 Si →+

SiF4

Linde.

0

100

200

300

400

500

600

700

800

900

1000

9200 9300 9400 9500 9600 9700 9800 9900 10000

inte

nsi

ty/

mV

magnet current/steps

SiF4 (Russ92), quartz vs. sapphire tube, cup config.: SiF3_1,2,3 (cup2), norm m/z = 86

SiF4 (Russ92), quartz tube

SiF4 (Russ92), sapphire tube

28Si19F3+

29Si19F3+

30Si19F3+

Ar2+


0.000 005 ≤ R ≤ 1

28Si 29Si 30Si

R

Classical Concept

0.1 ≤ R ≤ 70

IDMS

w(VE)

29Si 30Si

VE

R

28Si

Novel Concept

M(Si)

Virtual element

modified IDMS:virtual element


Why u(NA) = 2 x 10-8?Dissemination and uncertainty propagation









0 µg

6 µg

14 µg

25 µg

≤ 83 µg (E1)

6 µg


20 µg

44 µg

Ex. 1 (CCM req.)

30 µg

85 µg (E2)

Ex. 2

30 µg

71 µg

71 µg

77 µg


Ex. 3

42 µg

43 µg

32 µg

53 µg

≤ 83 µg (E1) 100 µg (E2)

30 µg

30 µg 43 µg

43 µg

71 µg

71 µg









0 µg

6 µg

14 µg

25 µg

≤ 83 µg (E1)

6 µg


20 µg

44 µg

Ex. 1 (CCM req.)

30 µg

85 µg (E2)

Ex. 2

30 µg

71 µg

71 µg

77 µg


Ex. 3

42 µg

43 µg

32 µg

53 µg

≤ 83 µg (E1) 100 µg (E2)

30 µg

30 µg 43 µg

43 µg

71 µg

71 µg

6 µg

6 µg

w


New concept II

Precondition: Si-material consists only of 28Si, 29Si and 30Si

1 = w28 + w30/29

M = x28 M28 + x29 M29 + x30 M30

R30/29 = n30 / n29

IDMS

Int. J. Mass Spectrom. 289 (2010) 47Int. J. Mass Spectrom. 291 (2010) 55.

. Int. J. Mass Spectrom. 299 (2011) 78Int. J. Mass Spectrom. 305 (2011) 58


-0.01

0.04

0.09

0.14

0.19

0.24

0.29

28.94 28.95 28.96 28.97 28.98 28.99 29 29.01 29.02 29.03 29.04

M /(g/mole)

ion

sign

al/V

Signal at mass 29 for natural material

200 ppb natural Si

29Si N2H

COH


Consequences

• Mu ≠ 1g/mol exact: lost of the direct relation between mol and kg

• NA has no more defined by kg

• Difference Mu(at present) und Mu(new) smaller than its uncertainty

• Probably a lost of understandability


Before and after definiton

M(A) = Ar(A) Mu g/mol molar mass

Mu = mu NA = 1 g/mol; U(Mu) = 0 molar mass const.

mu = m(12C)/12 g atomic mass const.

2)(

2

αecA

RhNM

r

Au

∞= U(Mu) ≠ 0after

defintion

Definition: M(12C) = 12 g/molFurthermore: Ar(12C) = 12Therefore: Mu = 1 g/mol

U(Mu) = 0 g/mol


First introduced by Ostwald 1893

Ar(A) relativ atomic masses (dimensionless)Mu molar mass constant (10-3 kg/mol)

Molar mass

Wilhelm Ostwald

Ulrich Stille

1808 Dalton: Hypothesis of atomistic nature of substances1893 Ostwald: Introduction of the molar mass1909 Einstein: Prove of the existence of atoms1955 Ulrich Stille: Introduction of the term „amount of substance“1967 Mole becomes the 7th SI unit

John Dalton

Albert Einstein


International Units System

Liminous intensity: candela

Amount of substance: mol

Temperature: kelvin

Electric current: ampere

Time: second

Mass: kilogram

Length : meter


History of NA-Measurement results

Loschmidt:Brown motion in gas

Einstein:Diffusion theory

Millikan:elementary charge

Bearden

Deslattes

∼∼∼∼10-1/15 a

year

rel.

unce

rtai

nty

Bragg:crystals

Silicon crystals

target: 2 ⋅⋅⋅⋅ 10-8

Peter Becker: The Avogadro Project: a 25 Year Quest, 20 Mai 2011, NIST


Zonefloating

N

H He

Li Be B C O F Ne

Na Mg Al Si P S Cl Ar

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

Fr Ra Ac

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Th Pa U

NB C O

Al Si P S

Ga Ge As Se

In Sn Sb Te

IR measured

depleted

Purity characterization

Sum electrical conductivity and parameter: crystal perfection


Na Mg Al Si P S Cl Ar

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

Fr Ra Ac

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu

Th Pa U

N

H He

Li Be B C O F Ne

LoD in the range of 10-6 –10-12 g/gPossible partner for

NAA: INRIMGDMS: PTB

Impurity determination by NAA and GDMS


60

mi

Rb1

Rz,28RzRx

Rbx

38.2 %

25.6 % 23.5 %

Uncertainty Calculation of Molar Mass: example budget

Uncertainty budget


Conclusion

Advantages• Solely R30/29 need to be measured• Only one chemical conversion• Blank substraction possible

Difficulties:• Extremly small 30Si and 29Si signals due to limited Si content of

the solutions (solubility, nebulizer capacity)• 29Si - 28SiH signal separation

Future work• Validation of the method

International cooperation, CCQM comparison• Gas mass spectrometry• New enriched material


Experimental

29 30 31 32

0.000

0.001

0.002

0.003

0.004

0.005

16O+

2

30Si+29Si

+U /

V

M / (g/mol)

H3 cup scan

„Si28“inw(NaOH) = 0.001 g/gvs.

NaOH(w = 0.001 g/g)

„Broadband interference“ induced by Na scattering

A. Pramann, O. Rienitz, D. Schiel: Anal. Chem. 84 (2012) 10175


Isotope dilution mass spectrometry

● primary method● analyte content

206Pb 208Pb

206Pb 208Pb

w(Pb)

1208/206 ≈R

206Pb 208Pb

X

Y

B206Pb 208Pb

206Pb 208Pb

w(Pb)

1208/206 ≈R

206Pb 208Pb

X

Y

B

Pb

Pb

PbPb

Pb IDMS

w(Pb)Pb

Pb

PbPb

Pb IDMS

w(Pb)

Metrologia 47 (2010) 460-463


Experimental

Main Improvement: Application of sodium-free solvents:

using tetramethylammonium hydroxide (TMAH)* instead of NaOH

TMAH

2-4

4- H2SiOOH 4 Si +→+

*Robert Vocke, Jr., Savelas Rabb, Gregory Turk: private communication (NIST, USA) 2011

Advantages of TMAH● higher signal intensity (factor 5)● MS does not suffer from clogging etc.● stable intensity over days● no more sodium in the plasma

(no scattering/broadband interference)


LatticeLatticeLatticeLattice parameterparameterparameterparameter determinationdeterminationdeterminationdetermination: : : : PrinciplePrinciplePrinciplePrinciple

This image cannot currently be displayed.This image cannot currently be displayed.

Combined optical and x-ray interferometry

1 cm

∆s

Deslattes 1973


Calibration

Mass discremination and fractionation requires calibration(Determination of K-factors)

R = I30/I29

Rmess= Imess,30/Imess,29

Imess,29 Imess,30

R / Rmess= K

ICPB


Calibration + IDMS

blend bxRbx

mw2

mx

mz1my1

blend b2Rb2

blend b1Rb1

myx

mz2

material yRy, Ry,28

material zRz, Rz,28

29Si 30Si28Si 29Si 30Si28Si

material wRw, Rw,28

29Si 30Si28Si

material xRx

29Si 30Si28Si


Partner Institute Method Status Publication

NIM (China) IDMS almost finished ?

NIST (USA) IDMS finished to be submitted

NMIJ (Japan) IDMS almost finished ?

NRC (Canada) IDMS finished published

PTB (Germany) IDMS finished published

International cooperation

68


Further interpretation of the XRCD experiment

• 12.058…….cm3 of 28Si at 20 oC in vacuum is 1 molwith an uncertainty of 2·10-8

• 2.152……..1025 atoms of 28Si are 1 kg with an uncertainty of 2·10-8

• 35.747……mol of 28Si atoms are 1 kg with an uncertainty of 2·10-8


2) m / M = n

N / NA = m / M


Watt balance experiment

In the weighing experiment, a mass and a coil are suspended from a balance. The coil (wire length L) is placed in a magnetic field of flux density B. The gravitational force on the mass m is balanced by an equal and opposite electromagnetic force on the coil by sending a current I through it:m g = I L B

In the moving experiment, the coil is moved at a vertical speed v through the magnetic field so that a voltage U is induced:U = B L v

Scematic principle taken from the BIPM website http://www.bipm.org/en/scientific/elec/watt_balance/wb_principle.html

NIST Watt balancehttp://www.google.de/imgres?imgurl=http://upload.wikimedia.org/wikipedia/commons/a/af/Watt_balance,_


Torch (sapphire body, BN shield)

„Si-free“ equipment

spray chamber (Peak and PFA body)

15 cm


Experimental

Sample preparation

● Cleaning & Etching of Si crystals

● Mass determination

● Dissolution in aqueous TMAH

Transformation in a single step!

2-4

4- H2SiOOH 4 Si +→+

OH 2H2SiFHF 6SiO 2-2

62 ++→+ +

OH HHNOSiFHHF 6HNOSi 222623 +++→++

400 mg


Experimental

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

H2O NaOH (0.01%) Merck

NaOH (0.1%) Merck

NaOH (0.1%) Fluka

NaOH (0.4%) Merck

NaOH (4%) Merck

NaOH (25%) Merck

30S

i/29S

i/(V

/V)

solvent

isotope ratios of aqueous NaOH: R = f(wNaOH)

R(30Si/29Si)

R(30Si/29Si)av (Sinat)

Isotope ratio dependence from w(NaOH)

30Si/29Si

average 30Si/29Si (natural Si)

A. Pramann, O. Rienitz, D. Schiel: Anal. Chem. 84 (2012) 10175


Two routes of measurement

Si (crystal)

Chemical conversion e.g. HF, BrF5

SiF4 (gaseous )

Gas MSmeasurement

Isotopic composition

Molar mass

Si (crystal)

Alkaline dissolutione.g. NaOH or TMAH

Si-solution (liquid )

ICP-MS measurement

Isotopic composition

Molar mass

Documents

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