Article pubs.acs.org/ac
Mass Spectrometric Investigation of Silicon Extremely Enriched in 28 Si: From 28SiF4 (Gas Phase IRMS) to 28Si Crystals (MC-ICP-MS) Axel Pramann* and Olaf Rienitz Physikalisch-Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany S Supporting Information *
ABSTRACT: A new generation of silicon crystals even further enriched in 28Si (x(28Si) > 0.999 98 mol/mol), recently produced by companies and institutes in Russia within the framework of a project initiated by PTB, were investigated with respect to their isotopic composition and molar mass M(Si). A modified isotope dilution mass spectrometric (IDMS) method treating the silicon as the matrix containing a so-called virtual element (VE) existing of the isotopes 29Si and 30Si solely and high resolution multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) were applied in combination. This method succeeds also when examining the new materials holding merely trace amounts of 29Si (x(29Si) ≈ 5 × 10−6 mol/mol) and 30Si (x(30Si) ≈ 7 × 10−7 mol/mol) extremely difficult to detect with lowest uncertainty. However, there is a need for validating the enrichment in 28Si already in the precursor material of the final crystals, silicon tetrafluoride (SiF4) gas prior to crystal production. For that purpose, the isotopic composition of selected SiF4 samples was determined using a multicollector magnetic sector field gas-phase isotope ratio mass spectrometer. Contaminations of SiF4 by natural silicon due to storing and during the isotope ratio mass spectrometry (IRMS) measurements were observed and quantified. The respective MC-ICP-MS measurements of the corresponding crystal samples show−in contrast−several advantages compared to gas phase IRMS. M(Si) of the new crystals were determined to some extent with uncertainties urel(M) < 1 × 10−9. This study presents a clear dependence of the uncertainty urel(M(Si)) on the degree of enrichment in 28Si. This leads to a reduction of urel(M(Si)) during the past decade by almost 3 orders of magnitude and thus further reduces the uncertainty of the Avogadro constant NA which is one of the preconditions for the redefinition of the SI unit kilogram. To that end, PTB started a project called “kilogram-2” (“kg2”) in 2012 with the goal to produce two additional silicon single crystals with even higher enrichment in 28Si than in the previous crystal in order to get four silicon spheres for the determination of NA. The detailed production process of the new crystals is described elsewhere.8 In brief, silicon crystal material with natural isotopic composition (x(28Si) = 0.922 mol/mol; x(29Si) = 0.047 mol/mol; x(30Si) = 0.031 mol/mol) was shipped from Germany to the company JSC PA “Electrochemical Plant” (ECP) in Zelenogorsk, Russia. There, this silicon was converted with purified fluorine gas to silicon tetrafluoride gas (SiF4), which was then enriched in 28Si with the aid of numerous cascades of gas centrifuges. This SiF4 enriched in 28Si was then converted to extremely pure silane (SiH4) at the Institute of Chemistry of High-Purity Substances (IChHPS RAS) of the Russian Academy of Sciences in Nizhny Novgorod, Russia. Subsequently, the SiH4 was deposited on a 28 Si single crystalline precursor rod using chemical vapor deposition in order to produce a polycrystalline silicon crystal of approximately 6 kg. Applying a float zone technique, this
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n reference to the upcoming redefinition of the SI unit of the mass, the kilogram, increased efforts are made in the fields of physics and chemistry relating to metrology. Fundamental constants like the Planck constant h or the Avogadro constant NA are best suited for the realization of the kilogram.1,2 One approach, the “Watt Balance” experiment has shown considerable improvements toward a determination of h with reduced uncertainty. 3 The competing, but also complementing approach, the X-ray crystal density (XRCD) method (“silicon-route” applied in the “Avogadro-Project”) is able to determine NA with the lowest associated uncertainty so far.4−7 One prerequisite for a redefinition of the kilogram will be the determination of NA with urel(NA) < 2 × 10−8. For this purpose, chemically ultrapure silicon single crystal material highly enriched in the 28Si isotope (amount of substance fraction x(28Si) > 0.9999 mol/mol) is used to determine NA via the relation NA = (NM)/(ρa3).7 Here, N represents the number of atoms per unit cell, M is the molar mass of the silicon crystal, ρ is its density, and a is the respective lattice parameter. Recently, NA was determined with an associated uncertainty urel(NA) = 2 × 10−8 using a single crystal with x(28Si) = 0.999 957 mol/mol corresponding to urel(M) = 5 × 10−9.7 A suitable way to further reduce urel(M) (and, therefore, urel(NA)) is an increased enrichment in 28Si with x(28Si) > 0.999 98 mol/mol. © XXXX American Chemical Society
Received: March 11, 2016 Accepted: May 13, 2016
A
DOI: 10.1021/acs.analchem.6b00971 Anal. Chem. XXXX, XXX, XXX−XXX
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national metrology institutes (NMIs): the National Research Council (NRC, Canada),15 the National Metrology Institute of Japan (NMIJ, Japan),16 the National Institute of Standards and Technology (NIST, U.S.A.)17 and, recently, the National Institute of Metrology (NIM, P. R. China).18 The measured isotope ratios Rmeas are affected by mass bias and must be corrected by calibration (K) factors. Analytical closed form expressions were developed allowing the accurate correction by calibration factors (K) to be determined in the very experiment.19 The Rmeas are related to the unbiased (in the following denoted as “true”) isotope ratios Rtrue = K × Rmeas using calibration factors K2 and K3 (for the ratios 30Si/29Si (index 2) and 28Si/29Si (index 3)). The measured ratios were determined from the respective ion intensities (voltages) in at least two blends. One consisting of a mixture of silicon with a natural isotopic composition and silicon (“Si29”) that is highly enriched in the 29Si isotope. The other blend consisting of a mixture of “Si29” (material z) and “Si30” (material y). A third blend is also possible using the materials y and w (natural silicon) and was prepared and measured, too.20,21
polycrystal was converted to a chemically extremely pure single crystal (>5 kg) at the Leibniz-Institute for Crystal Growth (IKZ) in Berlin, Germany. Finally, the spheres and additional parts were prepared at PTB ready to determine NA. Simulations had already demonstrated a decrease of urel(M) with increasing x(28Si) prior to the measurements. However, this extreme enrichment in 28Si causes considerably low abundances of the residual 29Si and 30Si isotopes, which means that their mass spectrometric detection might be even more difficult and will possibly increase the uncertainty. The current study shows that measurements of M of the new crystal materials from Russia (with x(28Si) ranging from 0.999 984 mol/mol to 0.999 994 mol/mol) result indeed in a reduction of urel(M) with increasing enrichment in 28Si, yielding urel(M) < 10−9, which is a milestone in the “Avogadro-Project” as well as in chemistry. For the first time, measurements of the crystals by MC-ICP-MS, able to correct for contamination by natural silicon, are compared to gas-phase IRMS measurements of some SiF4 precursor gas samples obtained from Russia. Due to the extremely limited material enriched in 28Si, high costs of this special material and high relevance for metrology within the context of the redefinition of the kilogram and mole, it was necessary to monitor the isotopic composition and enrichment in 28Si in the gas prior to the crystal production from the same starting material during the production process using gas phase IRMS. The detailed principle of the gas-phase IRMS measurements is described and advantages of MC-ICP-MS compared to gas-phase IRMS are highlighted and discussed. Measurement uncertainties were calculated according to the “Guide to the Expression of Uncertainty in Measurement” (GUM).9
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EXPERIMENTAL SECTION Reagents and Materials. Polycrystalline silicon samples were cut from parts of the crystal ingot prior to the float zone process, whereas single crystalline sample parts were cut from the final single crystal ingot (or test crystals) at IKZ. During the “kg-2”-project, three different batches (22, 23, and 24) were produced. For a clearer understanding, each batch and the production stage are indicated with a “SIS code” (Sample Identification System, see Table 1).8
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PRINCIPLE OF MOLAR MASS DETERMINATION IN SILICON CRYSTALS The basic concept of the molar mass determination in the silicon material enriched in 28Si is based on a modified IDMS principle using a “virtual-element” (VE).10,11 Briefly, the high enrichment in 28Si (x(28Si) > 0.9999 mol/mol) causes the problem of measuring isotope ratios (e.g., 30Si/28Si) far from unity associated with large uncertainties. In the VE-IDMS principle, this problem is solved by measuring only the so-called VE consisting of 29Si and 30Si in the matrix of the silicon material. The sum of the mass fractions w of 29Si and 30Si constitutes a kind of “impurity” in the silicon matrix. A 30Si spike (“Si30”, material highly enriched in 30Si) is used to spike the silicon sample enriched in 28Si (material x) forming an IDMS blend (bx). In the sample and the IDMS blend, the isotope ratios R(30Si/29Si) fell in the ranges of approximately 2−4 × 10−2 (x) and 1−5 (bx) and could be measured with relative uncertainties (k = 1) smaller than 1%, sufficient to yield urel(M(Si)) < 5 × 10−9. M(Si) and x(28Si), x(29Si), and x(30Si) are connected by the relation
Table 1. General Notation of Gas and Crystal Samples
∑ [x(iSi)·M(iSi)] i = 28
SIS code
SiF4 gas
polycrystal
single crystal
1st 2nd 3rd
Si28-22Pr Si28-23Pr Si28-24Pr
Si28-22Pr3 Si28-23Pr3 Si28-24Pr3
Si28-22Pr7 Si28-23Pr7 Si28-24Pr7
Si28-22Pr10/11 Si28-23Pr10/11 Si28-24Pr10/11
This means that the notation Si28-23Pr7 denotes a polycrystalline sample of the second batch. The first batch was produced for test purposes, whereas the second and third batches were made for the two final crystal ingots and the respective four spheres of the “kg-2”-project. The isotopic composition of poly- and single crystalline samples (approximately 200−500 mg) was measured arbitrarily to ensure the proper production of the final crystals. Prior to MC-ICP-MS measurements, the crystals were cleaned with ethanol (Merck p.a.: 99.9%), acetone (Merck p.a.: 99.8%), deionized (DI) water (generated via a Millipore water purification system with ρ ≥ 18 MΩ cm) and etched using an HF-containing mixture according to a procedure described elsewhere.22 After weighing and correcting for mass buoyancy, the crystals were dissolved in aqueous tetramethylammonium hydroxide (TMAH, Alfa Aesar, electronic grade 99.999%) and further diluted with DI water. Final liquid 28Si samples have mass fractions w in the range of 2000 to 4500 μg/g. Blends with silicon material enriched in 30Si used for the VE-IDMS-principle and solutions with silicon with natural isotopic composition for the determination of K factors were prepared as reported elsewhere.20,22 The SiF4 gas samples were obtained from ECP in gas cylinders (Monel) with volumes of 50 mL each (corresponding to 0.2 g SiF4 gas at p = 0.9 bar). These gas cylinders were prepared, cleaned and distributed by PTB. Passivation of the
30
M=
batch
(1)
i
where M( Si) are the respective molar masses of the three silicon isotopes.12,13 M(Si) is derived from eq 2 in ref 14. By determining the masses myx of the solid spike material y and mass mx of the solid sample material x in the IDMS blend bx and measuring the isotope ratios R2 = x(30Si)/x(29Si) and R3 = x(28Si)/x(29Si) in the respective endmember materials and blends, M(Si) is obtained. Meanwhile, these newly developed principles have been successfully applied and adopted by other B
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the current work is to measure absolute isotope ratios, no alternating measurements by switching from the sample bellow to the reference bellow were performed. The right bellow was used both for the reference gas as well as for the sample gas− even though “sample gas” and “reference gas” were the same. During one sequence, 10 cycles per method were carried out. Prior to each method, a peak center, background subtraction, and pressure adjustment were performed leading to a total duration of 1 h per sequence. Also, in gas phase IRMS experiments, measured isotope ratios Rmeas suffer from mass bias. In the case of the static operation mode, fragmentation is mainly affected by the ionization process. Usually, calibration (K) factors can be determined either numerically or analytically.19 In this study, a first attempt of (preliminary) calibration was made, when measuring commercial SiF4 gas (Linde, purity 99.995%, natural isotopic composition of Si) and adjusting the resulting isotopic composition with the respective reference values of natural silicon reported by IUPAC.24 Preliminary K factors used in this study were derived by the following relation:24
gas cylinders was performed by multiple charging and draining with SiF4 enriched in 28Si at ECP prior to the final filling. All cylinders were treated according the same protocol. Preliminary K factors for the mass bias correction of measured isotope ratios were derived using SiF4 gas from Linde (99.995%) with silicon having a natural isotopic composition, since a closedform approach as described for the MC-ICP-MS experiment is still lacking in the gas phase IRMS experiment. Gas Phase Isotope Ratio Mass Spectrometry of SiF4. The isotopic composition of Si in the SiF4 samples was measured using a commercial multicollector stable isotope ratio mass spectrometer, MAT 253 (Thermo Fisher Scientific GmbH, Bremen, Germany), equipped with a dual inlet gas sample introduction system.23 Table 2 summarizes typical main operation parameters. Table 2. Parameters of the MAT 253 Used for SiF4 Measurements mass resolution M/ΔM mass range m/z Faraday cups (in parallel) acceleration voltage (kV) ionization type electron energy (eV) entrance slit (μm) exit slit (mm) Dual Inlet Device bellow volume (mL) bellow used measurement mode inlet pressure p0 (mbar)
200 1−150 9 9.499 electron impact 81.75 200 1.5−2.2
K = RIUPAC/Rmeas , with Rmeas = I(29Si)/I(28Si) and Rmeas = I(30Si)/I(28Si))
MC-ICP-MS Measurements. The liquid samples (w(Si) ≈ 2000−4500 μg/g in aqueous TMAH with w(TMAH) = 0.0006 g/g) were measured using a commercial high resolution MCICP-MS (Neptune, Thermo Fisher Scientific GmbH, Bremen). The main operation and machine parameters are given elsewhere.14,21 All measurements in this study were performed in the high resolution (HR) static mode with M/ΔM = 8000. The samples were bracketed by blank solutions of aqueous TMAH with w = 0.0006 g/g. Both blanks and corresponding samples were measured using the same method. Between the pairs of blanks and samples, the tubings of the sample inlet were rinsed with DI water to get rid of cross contaminations by silicon of natural isotopic composition. Each sample and corresponding blank were measured four times using a method consisting of six blocks with three cycles per block (integration time: 4 s). Due to the extreme enrichment in 28Si, the respective Faraday detector was moved out of the beam, and only the isotopes 29Si and 30Si were measured to receive the isotope ratios Rmeas = I(29Si)/I(30Si) in the sample (x), IDMS blend (bx), calibration solution (w), and respective blanks.
40 right (only) static 10−15
The MAT 253 was specially designed for the measurement of SiF4 gases with extremely different abundances of the three respective isotopes of silicon (28Si, 29Si, and 30Si) with x(iSi) ranging from x = 0.01−0.99 each. For the purpose of best amplification within the dynamic range, an array of nine tailored Faraday cups was engineered, connected to, in some cases, various resistors. Three Si isotopes can be measured simultaneously. In order to reduce the contamination of SiF4 by natural silicon, several Si containing parts in the MAT 253 were exchanged, for example, the gas inlet tube from the dual inlet device (originally made of quartz) was replaced by a sapphire tube. Table 3 shows the typical focus settings applied in the MAT 253 software. All SiF4 measurements were carried out applying a method using 26 s integration time. Since one aim of
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RESULTS AND DISCUSSION Calibration of Isotope Ratio Measurements Using the MAT 253. K factors of the gas phase experiments were determined in 10 measurements using the Linde SiF4 gas, as described above. Uncertainties associated with x(iSi) of the respective silicon isotopes as well as for the K factors were calculated using the GUM Workbench 2.4 Pro Software.25 For the uncertainty calculations of the “measured” x(28Si), x(29Si), and x(30Si), standard uncertainties of the resistor of the respective Faraday cup collecting this ion were estimated. In these budgets, uncertainties of about 1% of the value of the respective resistor (e.g., 3 × 108 Ohm) were applied in order to account conservatively for this contribution. Once the “measured” x(iSi) (with associated uncertainties) were determined, another uncertainty budget was set up implementing the “true” isotope ratios and associated uncertainties (given by IUPAC) yielding the K factors (with associated uncertainties) for the ratios 29Si/28Si and 30Si/28Si. Table 4
Table 3. Typical Focus Settings of the MAT 253 Used for SiF4 Measurements emission (mA) trap (V) electron energy (V) extraction (%) shield (%) X-focus (%) X-focus sym. (%) R-plate (%) Y-deflection (%) deflection sym. (%) Einzel lens (%) Einzel lens sym. (%)
1.5 12.9 81.746 40.00 100 6.325 −0.855 44.64 4.6 −8.1 25.8 −15.1 C
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energetic regime, dissociative ionization of SiF4 leads to the predominant formation of the singly charged SiF3+, due to its inherently high ionization cross section. Besides the SiF3+ ion, a number of fragment ions can be detected, both singly charged (SiF2+, SiF+, Si+, F+, and also SiF4+ in significant abundance) as well as doubly charged (SiF32+, SiF22+, SiF2+, and Si2+). While changing the ionization conditions, always the same fragmentation pattern has been observed and it is worth to note that the distribution of fragment ion intensities (normalized to the intensity of the SiF3+ ion) of the SiF4 measured in this study agrees almost perfectly with a mass spectrometric study of SiF4 with natural composition reported by Beattie. 28 The normalized intensities are plotted in Figure 2 below the ion notation (values from ref 28 in brackets). The gas phase IRMS measurements were focused on the most abundant SiF3+ ion consisting of the ions 28Si19F3+ (m/z = 85), 29Si19F3+ (m/z = 86), and 30Si19F3+ (m/z = 87). In Figure 3, a typical mass scan of SiF4 (SIS code Si28-24Pr3.1) shows
Table 4. Isotopic Composition of SiF4 Gas (Linde) with Natural Isotopic Composition Compared to IUPAC Data24,a Linde (avg) IUPAC a
x(28Si)/(mol/mol)
x(29Si)/(mol/mol)
x(30Si)/(mol/mol)
0.922 69(88) 0.922 23(19)
0.047 04(62) 0.046 85(8)
0.030 26(41) 0.030 92(11)
Uncertainties in parentheses (k = 1) apply to the last digits.
displays the average values of x(iSi) of the Linde gas measurements in comparison to the IUPAC data.24 The following K factors were derived: K(29Si/28Si) = 0.996(13) (mol/mol)/(V/V) and K(30Si/28Si) = 1.022(14) (mol/mol)/ (V/V). Numbers in parentheses denote uncertainties of the last digits (k = 1). Although the numerical value of, for example, x(30Si), Linde, differs by 2% from x(30Si), IUPAC, a proper agreement (at least for k = 2) is ensured within the limits of the uncertainties (Figure 1).
Figure 1. Measured x(29Si) vs x(30Si) of silicon in the SiF4 gas (Linde) with natural isotopic composition compared to IUPAC data.24 Error bars indicate combined uncertainties (k = 1).
Figure 3. Mass scan of an SiF4 sample (Si28-24Pr3.1) in the range m/ z = 85−87.
The isotope ratios 29Si/28Si and 30Si/28Si of the different measurements of the respective gas cylinders were then finally corrected using the above K factors. Mass Spectrometry of SiF4 Using the MAT 253. Figure 2 shows a typical mass spectrum (magnet scan) of the SiF4 enriched in 28Si measured at an electron impact energy of 81 eV. As described by Basner et al. and Gonfiantini,26,27 in this
the peaks (plateaus) in the mass range between m/z = 85 and 87. Due to the high enrichment of the 28Si isotope and thus high abundance of the 28Si19F3+ ion, the respective peak is cut off. More notable is the relative abundance of the 29Si19F3+ and 30 19 + Si F3 ions and their isotope ratio. At a first glance, a ratio 29 Si/30Si ≈ 2 can be estimated. Another observation is a tailinglike effect toward higher masses arising from the extremely intense 28Si19F3+ ion superpositioning with the intensities of 29 19 + Si F3 and 30Si19F3+ at m/z = 86 and 87. Figure 4 displays x(28Si) in the first SiF4 sample cylinder (Si28-24Pr3.1.1) measured during 39 runs. During the first ten runs, no constant x(28Si) can be observed, mainly caused by insufficient passivation of the gas tubes of the MAT 253 during the intervals of the single runs. Therefore, the mass spectrometer was rinsed with the sample gas continuously overnight. As a consequence, a sudden onset in x(28Si) was observed, equilibrating after approximately 30 runs. Additional rinsing did not increase x(28Si) further. This effect is a clear indication of contamination by natural silicon in the gas tubings of the MAT 253. Figure 5 shows the selected data of both SiF4 samples (cylinder 01, Si28-24Pr3.1.1; cylinder 02, Si28-24Pr3.1.2) with the associated uncertainties (k = 1). The ratio 29Si/30Si ≈ 2 in the SiF4 samples seems to be significantly smaller than expected when comparing with the respective isotope ratios of gases from the same batches, but from different larger gas cylinders measured at ECP (using a
Figure 2. Mass scan of SiF4 sample gas enriched in 28Si showing the distribution of singly and doubly charged fragment ions. Numbers below and numbers in brackets denote the respective ion intensities (normalized to SiF3+) found in this study and reported elsewhere.28 D
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mass scans for the identification of possible hydrides were carried out. Applying mass resolutions M/ΔM between 10000 and 40000, no noticeable or significant interferences, at least no hydrides, in the vicinity of m/z = 86 and 87 could be detected. Prior to each measurement, the H2O background was measured in the scanning mode. A sequence with the MAT 253 (a scan with the DFS, respectively) was started only, when the H2O+ signal was below 20 × 10−6 of the most abundant SiF3+ signal. The DFS results gave an indication that the biased isotope ratio must have other origins, most notably: the storage conditions in the gas cylinder of this highly reactive gas, and additionally, contamination due to natural silicon caused by the MAT 253 itself during the measurement. A comparison with MC-ICP-MS results and a quantitative estimation of the contamination with natural silicon is given below. Calibration of Isotope Ratio Measurements Using the MC-ICP-MS. In the materials w, y, and z as well as in the blends of these materials, the isotope ratios R2 = I(30Si)/I(29Si) meas meas and K3 = Rtrue and R3 = I(28Si)/I(29Si), K2 = Rtrue 2 /R2 3 /R3 were determined analytically, with the aim to obtain the “true” true isotope ratios Rtrue y,2 and Ry,3 of “Si30”, the spike material, and true Rw,2 , the reference material. In order to obtain the K factors for mass bias correction, six sequences were measured. All 12 possible options with pairs of K2 and K3 values were calculated, and the result with the smallest associated uncertainty was chosen.21 Mass Spectrometry of Si Crystals Using the Neptune MC-ICP-MS. During the production of the final “kg-2” single crystals (second and third batch), several spot tests (e.g., the single crystalline test crystal (Si28-22Pr10) of the first batch; a single crystalline test crystal (Si28-23Pr10) of the second batch; and the polycrystalline precursor crystal (Si28-24Pr7) of the third batch) were performed to determine the respective molar mass and isotopic composition. In preceding measurements of the SiF4 gases of the respective batches using a gas-phase IRMS described above, the isotopic composition has been determined by the Russian project partners and by PTB in order to validate the progress of the crystal production. These gas-phase IRMS results predicted x(28Si) ≈ 0.999 98 mol/mol (first and second batch) up to x(28Si) > 0.999 99 mol/mol in the third batch. This elevated enrichment in 28Si compared to the first “Avogadro” crystal (Si28-10Pr11) enriched in 28Si implies the depletion of the sum of x(29Si) and x(30Si) in the new crystals which might complicate the detection of these two important isotopes which are present in ultratrace amounts (x(29Si) ≈ 5 × 10−6 mol/mol; x(30Si) ≈ 7 × 10−7 mol/mol). These are extremely difficult to detect and thus may increase the associated uncertainty. However, the recent measurements and results of the “kg-2” crystals show that they can be determined at least as accurately as those of the first “Avogadro” crystal (x(28Si) = 0.999957 mol/mol). For a deeper insight into the amount of the blank signal, its contribution to the sample signal correction, and the stabilities of signal intensities, a Supporting Information file (SI) was added to the manuscript, including the raw data of the MCICP-MS measurements and the calculations of molar masses and amount-of-substance fractions. The enrichment in x(28Si) of the different crystals of the “kg-2” project compared to the first “Avogadro” crystal enriched in 28Si is displayed in Figure 6. A clear increase in the enrichment in 28Si can be observed indicating at a first glance that the “kg-2” project succeeded in realizing the extended enrichment in 28Si while decreasing the measurement uncertainty. Figure 7 shows a comparison of the
Figure 4. Course of x(28Si) in SiF4 (Si28-24Pr3.1.1, first of two gas cylinders) during 39 runs. After the tenth run, the MAT 253 was purged with SiF4 overnight. The last nine data points were selected for further evaluation.
Figure 5. Selected data of both SiF4 samples (dots: cylinder 01, Si2824Pr3.1.1; triangles: cylinder 02, Si28-24Pr3.1.2) with the associated standard uncertainties (k = 1).
single collector magnetic sector gas phase IRMS; 29Si/30Si ≈ 7) and at IChHPS RAS (using a high resolution single collector magnetic sector ICP-MS after transformation of SiF4 into a solution; 29Si/30Si ≈ 12) independently.29 One problem, when dealing with isotopes with artificially changing compositions, as in the case of the highly enriched 28Si, is related to mass interferences when operating with a relatively low mass resolution as in the case of the MAT 253. The main interferences we have to take care of in the range m/z = 85− 87 are the hydrides 28Si1HF3+ and 29Si1HF3+ with Δm/z to the respective SiF3+ ion ranging between Δm/z = 8 × 10−3 and 10 × 10−3. To resolve the hydrides, a mass resolution of approximately M/ΔM ≈ 10400 is necessary. To clarify the possible presence of interferences in the mass spectra of the SiF4 enriched in 28Si, scanning measurements of SiF4 gas were carried out at Thermo Fisher Scientific GmbH, Bremen (Germany) with a high resolution magnetic sector-field mass spectrometer (Thermo Fisher DFS). The DFS is operated also with an electron impact ionization source (although in a miniaturized manner). Since the DFS is not suited for isotope ratio measurements, only E
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success of the “kg-2” project, initially aiming at silicon crystals with reduced uncertainties. A recent “breakthrough” during the “Avogadro” project came up from results of the polycrystal of the third batch (Si28-24Pr7): for the first time, a molar mass with urel(M) < 1 × 10−9 has been determined at PTB in silicon highly enriched in 28Si (in that measurement series in a single case urel(M) = 5 × 10−10 was obtained). This extremely low uncertainty is directly related to the extreme enrichment in 28Si of that very material: x(28Si) = 0.999 994 751(20) and the improved VE-IDMS-method and MC-ICP-MS-technique. Table 5 shows a representative uncertainty budget of a crystal sample of the third batch (Si28-24Pr7). Compared to uncertainty budgets of the first “Avogadro” crystal, the main uncertainty contributions are generated by the measured meas isotope ratios Rmeas x,2 (58%) in the sample and Rbx,2 (26%) in the IDMS blend which are mainly caused by the absolute intensities of the signals and reproducibility of the isotope ratios.21 A smaller influence comes from the corrected isotope ratio Rw,2 (13%) of the natural silicon sample used to “calibrate” the IDMS sequence. No weighing result influences the budget of M any longer as in the case of the first “Avogadro” crystal enriched in 28Si encircling and improving the sources of uncertainties in molar mass determination. The uncertainty associated with the molar mass of silicon has decreased by almost 3 orders of magnitude which is a result of the improved material properties of the silicon crystals produced during the “kilogram-2” project compared with the first “Avogadro” crystal material enriched in 28Si; as well as improved methodologies and measurement techniques. In comparison, in 2003 the molar mass of silicon with natural isotopic composition was reported with urel(M) = 3 × 10−7 using silicon with a natural isotopic composition (“WASO”), measured at the Institute for Reference Materials and Measurements (EC-JRC-IRMM, Belgium).30 A decreasing uncertainty associated with M can be deduced from both improved material properties (increasing enrichment in x(28Si)) and further improved capabilities of the measurement of the molar mass developed at PTB. Quantification of Contamination of SiF4 Gas Enriched in 28Si by Natural Silicon. Table 6 shows the results of the MAT 253 measurements of the SiF4 samples (Si28−24Pr3.1) compared to the result of the MC-ICP-MS measurement of the corresponding polycrystal (Si28-24Pr7.3.1). The main interesting quantity is x(28Si) as a direct probe of its enrichment. A clear bias between the SiF4 and crystal measurements can be
Figure 6. x(28Si) of the single and polycrystals of the different batches (1st, 2nd, and 3rd) of “kg-2” compared to the first single crystal enriched in 28Si of the “Avogadro” project. Associated uncertainties u(x) are not resolved due to the scaling of the plot, but indicated numerically (k = 1).
Figure 7. Molar mass M of the single crystals and polycrystals of the different crystal batches (1st, 2nd, and 3rd) of “kg-2” and the “Avogadro” project. Associated uncertainties u(M) are not resolved due to the scaling of the plot, but indicated numerically (k = 1).
molar masses of the first “Avogadro” crystal enriched in 28Si with the crystals of the respective batches of the “kg-2” project. The associated uncertainties are too small to be resolved on the scale of this plot. Generally, the absolute value of the molar mass of the respective crystal decreases with increasing enrichment in x(28Si). Also, the uncertainties associated with M decrease with increasing x(28Si). This indeed expresses the
Table 5. Typical Uncertainty Budget of M (Crystal Sample of Si28-24Pr7, 3rd Batch “kg-2”) quantity Xi
unit [Xi]
best estimate (value) xi
std uncertainty u(xi)
sensitivity coefficient ci
index (%)
M(28Si) myx mx M(29Si) M(30Si) Ry,3 Ry,2 Rx,2meas Rbx,2meas Rw,2 Rw,2meas, IDMS Y M
g/mol g g g/mol g/mol mol/mol mol/mol V/V V/V mol/mol V/V [Y] g/mol
27.97692653494 4.603300 × 10−6 0.18189014 28.97649466909 29.9737701360 1.5855 269.04 0.09818 5.1660 0.66230 0.705440 y 27.9769322535
540 × 10−12 578 × 10−12 1.66 × 10−6 610 × 10−12 27.0 × 10−9 0.0222 5.65 2.05 × 10−3 0.0121 1.32 × 10−3 440 × 10−6 uc(y) 27.3 × 10−9
1.0 1.2 −31 × 10−6 4.8 × 10−6 260 × 10−9 −20 × 10−9 580 × 10−12 10 × 10−6 −1.1 × 10−6 −7.5 × 10−6 7.0 × 10−6
0.0 0.0 0.0 0.0 0.0 0.0 1.4 58.2% 25.9 13.1 1.3
F
DOI: 10.1021/acs.analchem.6b00971 Anal. Chem. XXXX, XXX, XXX−XXX
Article
Analytical Chemistry
Table 6. Results of Measurements of the Gas Samples (Si28-24Pr3.1.1 and 3.1.2) Enriched in 28Si Using an MAT 253 and the Polycrystalline Sample (Si28-24Pr7.3.1) Measured Using the MC-ICP-MSa cyl. 1 cyl. 2 polycrystal a
x(28Si)/(mol/mol)
x(29Si)/(mol/mol)
x(30Si)/(mol/mol)
n(29Si)/n(30Si) (mol/mol)
0.999 985 18(24) 0.999 985 37(23) 0.999 994 751(20)
0.000 009 88(19) 0.000 009 79(19) 0.000 004 815(16)
0.000 004 940(98) 0.000 004 839(96) 0.000 000 434(10)
2.0 2.0 11.1
Uncertainties in parentheses (k = 1) apply to the last digits.
observed. Whereas the gas phase IRMS measurements enable a detection of x(28Si) = 0.999 9 mol/mol, the application of the improved VE-IDMS method using an MC-ICP-MS resolves the full enrichment in x(28Si) = 0.999 99 mol/mol! The potential of the MC-ICP-MS measurement is based on the fact that most of the contamination with natural silicon is recorded by measuring the matrix-matched blank (aqueous TMAH) under exactly the same conditions as the sample. Thus, the blank data can be subtracted from the sample data. This is indeed not possible when using a gas mass spectrometer. Since systematic experimental causes for bias in the isotope ratio and thus x(iSi) determined by MAT 253 measurements compared to the MC-ICP-MS result can be excluded (e.g., hidden interferences as discussed), the origin can be clearly deduced from contamination of the SiF4 samples highly enriched in 28Si by the ubiquitous silicon having natural isotopic composition. It has to be clarified whether the contamination has been introduced during the storage or during the measurement with the MAT 253 or both. The effect of the contamination of the silicon highly enriched in 28Si with “natural” silicon (Sinat) can be calculated using the following equation, which estimates the mass of natural silicon necessary to observe the isotope ratio R30/29 in the gas, instead of the respective ratio of the same final crystal material measured using an MC-ICP-MS mbl = m x ·
M(Si nat) · Mx
meas x x( Si) − R30,29 ·x x(29Si) meas R30,29 ·xnat(29Si) − xnat(30Si)
Figure 8. Simulation of the isotope ratio R(29Si/30Si) of the silicon sample material highly enriched in 28Si vs the mass mbl of natural silicon theoretically contaminating that sample. The curve is plotted for an initial mass mx = 51 mg of the “theoretically” solid silicon enriched in 28Si necessary to prepare the SiF4 gas in the cylinder.
solid sample. This illustrates the extreme sensitivity of the silicon sample material enriched in 28Si to contamination by natural silicon.
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CONCLUSIONS The basic theoretical and experimental methods developed at PTB in order to determine the molar mass (M) and isotopic composition (x) of silicon highly enriched in 28Si in order to determine NA with reduced measurement uncertainty have been successfully applied to silicon crystals even further enriched in 28Si, produced during the “kg-2” project. A clear dependence of the uncertainty associated with the molar mass M from the enrichment in x(28Si) can be observed. In the latest crystal of the “kg-2” project with x(28Si) = 0.999 994 751(20), urel(M) = 9.8 × 10−10 was determined. This result was made possible using the further developed techniques of the VEIDMS principle accompanied by MC-ICP-MS for isotope ratio mass spectrometry which can still be applied to the new materials, though 29Si and 30Si are abundant at even more depleted ultratrace levels. The application of these techniques to the new silicon materials provides uncertainties on a level, which are, to the authors’ knowledge, unique in chemistry. The crystal measurements are accompanied by measurements of the gaseous SiF4 precursor materials of the respective batch using an MAT 253 and a clear contamination with silicon of natural composition has been deduced. In the gas phase experiments, there is no proper way to correct for this contamination by measuring, for example, the blank. Another origin of the contamination is the high reactivity of SiF4 releasing natural silicon from the surfaces of the MAT 253. An analytical approach to the estimation of the amount of the contaminating natural silicon has been developed. The use of a gas phase IRMS as a time saving MS technique (no conversion or preparation of the gas analyte) as a tool of an at first glance
30
(2)
where mbl is the mass of the unknown contaminating natural silicon in the sample enriched in 28Si, mx is the mass of the initial “theoretical” solid silicon crystal enriched in 28Si used for the preparation of the SiF4 in the gas cylinder. M(Sinat) is the molar mass of silicon with natural isotopic composition, Mx is the molar mass of the sample material highly enriched in 28Si (known from the MC-ICP-MS experiments), xx(29Si) and xx(30Si) are the known amount-of-substance fractions of the 29 Si and 30Si isotopes of the sample material highly enriched in 28 Si also known from MC-ICP-MS measurements, xnat(29Si) and xnat(30Si) are those of natural silicon, respectively. Finally, Rmeas 30,29 is the measured isotope ratio in the sample material enriched in 28Si using gas phase IRMS. The following example might illustrate this effect of contamination and is displayed in Figure 8, simulated using the relation meas R30/29
=
mx ·x (30Si) Mx x mx ·x (29Si) Mx x
+ +
mbl ·x (30Si) M(Si nat) nat mbl ·x (29Si) M(Si nat) nat
(3)
If mx = 51 mg of “Si28” crystal material highly enriched in Si with an isotope ratio R29,30 = 11 (Si28-24Pr7) was used for the preparation of the SiF4 in the gas cylinder and the gas phase IRMS measurement gives R29,30 = 2, the result can be explained by a potential contamination mbl = 13.5 μg of natural silicon which is only 0.026% of the mass of the “theoretically” initial 28
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DOI: 10.1021/acs.analchem.6b00971 Anal. Chem. XXXX, XXX, XXX−XXX
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(11) Pramann, A.; Rienitz, O.; Schiel, D.; Schlote, J.; Güttler, B.; Valkiers, S. Metrologia 2011, 48, S20−S25. (12) Wang, M.; Audi, G.; Wapstra, A. H.; Kondev, F. G.; MacCormick, M.; Xu, X.; Pfeiffer, B. Chin. Phys. C 2012, 36, 1603− 2014. (13) Taylor, B.; private communication. (14) Pramann, A.; Rienitz, O.; Schiel, D.; Güttler, B.; Valkiers, S. Int. J. Mass Spectrom. 2011, 305, 58−68. (15) Yang, L.; Mester, Z.; Sturgeon, R. E.; Mejia, J. Anal. Chem. 2012, 84, 2321−2327. (16) Narukawa, T.; Hioki, A.; Kuramoto, N.; Fujii, K. Metrologia 2014, 51, 161−168. (17) Vocke, R. D., Jr.; Rabb, S. A.; Turk, G. C. Metrologia 2014, 51, 361−375. (18) Ren, T.; Wang, J.; Zhou, T.; Lu, H.; Zhou, Y.-j. J. Anal. At. Spectrom. 2015, 30, 2449−2458. (19) Mana, G.; Rienitz, O. Int. J. Mass Spectrom. 2010, 291, 55−60. (20) Pramann, A.; Rienitz, O.; Noordmann, J.; Güttler, B.; Schiel, D. Z. Phys. Chem. 2014, 228, 405−419. (21) Pramann, A.; Lee, K.-S.; Noordmann, J.; Rienitz, O. Metrologia 2015, 52, 800−810. (22) Pramann, A.; Rienitz, O.; Schiel, D.; Güttler, B. Int. J. Mass Spectrom. 2011, 299, 78−86. (23) Brand, W. A. Mass Spectrometer Hardware for Analyzing Stable Isotope Ratios. In Handbook of Stable Isotope Analytical Techniques; Groot, P. A., Ed.; Elsevier, 2004; Vol. I. (24) De Laeter, J. R.; Böhlke, J. K.; De Bièvre, P.; Hidaka, H.; Peiser, H. S.; Rosman, K. J. R.; Taylor, P. D. P. Pure Appl. Chem. 2003, 75, 683−800. (25) GUM Workbench Pro software, version 2.4.1 392; Metrodata GmbH, Germany. (26) Basner, R.; Schmidt, M.; Denisov, E.; Becker, K.; Deutsch, H. J. Chem. Phys. 2001, 114, 1170−1177. (27) Gonfiantini, R.; private communication. (28) Beattie, W. H. Appl. Spectrosc. 1975, 29, 334−337. (29) Arefyev, D. (ECP); Potapov, A. (IChHPS RAS); private communication. (30) Becker, P.; Bettin, H.; Danzebrink, H.-U.; Gläser, M.; Kuetgens, U.; Nicolaus, A.; Schiel, D.; De Bièvre, P.; Valkiers, S.; Taylor, P. Metrologia 2003, 40, 271−287.
quality control instrument during the production process of the gas isotopically high enriched in 28Si giving at least a lower limit of enrichment in 28Si is nevertheless rational and indispensable. In the near future, also homogeneity studies of M and x(iSi) throughout the original silicon crystal using MC-ICP-MS are scheduled for monitoring these materials enriched in 28Si. Using the new silicon crystals, the molar mass will have an even more reduced contribution to the uncertainty of NA, supporting the redefinition of the kilogram.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.analchem.6b00971. Raw data of the MC-ICP-MS measurements of the discussed silicon crystals highly enriched in 28Si; calculations of molar masses and amount-of-substance fractions (XLSX).
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors gratefully acknowledge the important initial technical advices given by Ian Bateman and Peter Dijkman (both Thermo Fisher Scientfic) when starting the MAT 253 measurements of the “unknown” SiF4. Discussions with Jens Radke, Andreas Hilkert, and Dirk Krumwiede (all Thermo Fisher Scientific GmbH, Bremen, Germany) were gratefully acknowledged. In place of all our colleagues of the “Kilogram2”-project, we thank Peter Becker, Horst Bettin, Manfred Peters, and Detlef Schiel from PTB.
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REFERENCES
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DOI: 10.1021/acs.analchem.6b00971 Anal. Chem. XXXX, XXX, XXX−XXX
