x-ray crystal density method to determine the … constant definition of avogadro constant na •...
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X-ray Crystal Density Method to
Determine the Avogadro and Planck Constants
Horst BettinPhysikalisch-Technische Bundesanstalt
Braunschweig, Germany
Proposed New Definition of the Kilogram
The kilogram, symbol kg, is the SI unit of mass. It is defined
by taking the fixed numerical value of the Planck constant h
to be 6.626 070 040 x 10-34 when expressed in the unit J s,
which is equal to kg m2 s-1, where the metre and the second
are defined in terms of c and ∆νCs.
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*) X represents one or more digits to be added at the time the new definition is finally adopted.
∞
=R
cMhN
2
)(e-2
A
α
NAh = 3.990 312 7110(18) × 10−10 Js/mol,
with relative uncertainty of 0.45 × 10-9Amedeo Avogadro
(1776-1856)
Max Planck
(1858-1947)
Avogadro Constant
Definition of Avogadro constant NA
• Number of molecules per mol
• 6.022... x 1023 mol-1
Current definition of molAmedeo Avogadro
(1776-1856)
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• Number “entities” like 12C atoms in 12 g
• i. e. 6.022... x 1023 12C atoms have a mass of 12 g
12 g/mol = NA m(12C )
Faraday constant F = NA e (e: elementary charge)
Molar gas constant R = NA k (k: Boltzmann constant)
Counting Atoms: XRCD Method
1. Volume a03 of the unit cell
2. Volume of an atom: a03 /8
3. Volume V of a sphere
4. Number N of the atoms
Use of a silicon crystal!
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30
8
aV
N =sphere
molA m
MaV
N ⋅=30
8
Lattice parameter measurement (INRIM)
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d220(2014)=192014711.98(34) am
d220(2011)=192014712.67(67) am
ur(2014) = 1.8 x 10-9
Sphere Interferometer of PTB
Camera 1 Camera 2
mK-temperature stabilisation
Collimator
Fizeau-Objective 1
Fizeau-Objective 2
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Diode laser
Diameter results (2014)
Sphere Lab. Mean apparent diameter/nm
Relative Uncertainty
in 10-9
AVO28-S5c PTB 93 710 811.38(83) 9
AVO28-S5c NMIJ 93 710 811.11(62) 7
AVO28-S5c
weighted mean
93 710 811.21(50) 5
AVO28-S8c PTB 93 701 526.24(66) 7
AVO28-S8c NMIJ 93 701 526.29(68) 7
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AVO28-S8c NMIJ 93 701 526.29(68) 7
AVO28-S8c
weighted mean
93 701 526.26(47) 5
u(volume) = 1.5 x 10-8 V
Molar Mass Determination
Modified IDMS: virtual element
approach
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- Three samples: 28Si-material („x“) 30Si-enriched („y“)
IDMS-blend („bx“)
- R(30Si/29Si) measured in x, y, bx
MSi
A. Pramann et al.
Metrologia 48 (2011) S20-S25
5.0E-08
5.0E-07
1 2 3 4 5(S
i))
2.7 x 10-7
2003 2011 2014 2015 2015
Si28-10Pr11„Avogadro“
PTB
Si28-23Pr10„kilogram-2“
PTB
Si28-24Pr7„kilogram-2“
PTB
WASOIRMM
2016
Molar Mass Uncertainty
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5.0E-10
5.0E-09
ure
l(M(S
i))
8.2 x 10-9
4.4 x 10-9
3 x 10-9
9.8 x 10-10
99.995 % 99.998 % 99.9995 %28Si: 92 %
Mass Determination (at BIPM)
Sartorius CCL 1007 mass comparatorwith its vacuum transfer system
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Surface artefacts∆S = 186 cm2
Mass
Mass measurements
• Extraordinary calibrations using the IPK
• Uncertainty of the weighted mean: 3.5 µg
0.999698445
0.999698450
NMIJ
0.999401325
0.999401330
5 µg
Sphere AVO28-S5 Sphere AVO28-S8
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PTB
BIPM
NMIJ
WM
0.999698420
0.999698425
0.999698430
0.999698435
0.999698440
m/ k
g
5 µgBIPM
NMIJ
PTB
WM
0.999401300
0.999401305
0.999401310
0.999401315
0.999401320
m/ k
g
5 µg
Surface Characterisation
XRR/XRF
Carbon
Water
Si oxide
XRF, XPS, IR15 µg
Gravimetric8 µg
XPS, XRF,XRR, SE
70 µg
MethodMassSurface
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Ellipsometry
XRR/XRF
Metals
Si crystal
XRF< 1 µg
Quantity Relative uncertainty/10-9 Contribution/%
Molar mass 5 6
Lattice parameter 5 6
Surface 10 23
Uncertainty budget (2014)
Only one sphere (AVO28-S5c):
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Surface 10 23
Sphere volume 16 59
Sphere mass 4 4
Point defects 3 2
Total 21 100
Values of the Planck Constant (2016)
6,6260696
6,6260698
6,6260700
6,6260702
6,6260704/ k
g m
2s-
1
NIST-32014
IAC
NRC 2014
IAC 2014 CODATA
2014
Page 16 of 19
6,6260688
6,6260690
6,6260692
6,6260694
6,6260696
1034
h/ k
g m
IAC2010 NIST-4
2016
Improvements until June 2017
Aim: Avogadro value with relative uncertainty below 1.5 x 10-8
Improvements:
a) New XPS/XRF apparatus for spheres at PTB
b) New XPS apparatus for spheres at NMIJ
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c) Spheres with better roundness (smaller wavefront abberration)
d) New lattice parameter measurement at PTB
e) Avogadro constant determined using Si-28 with higher enrichment
Thank you very much for your attention!
Questions?
Comments?
Physikalisch-Technische BundesanstaltBraunschweig und BerlinBundesallee 10038116 BraunschweigGermany
Dr. Horst BettinWorking Groups “Solid State Density” and “Avogadro Constant”Telephone: +49 531 592-3330E-Mail: [email protected]
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