Vol.:(0123456789)1 3

Accreditation and Quality Assurance (2019) 24:329–339 https://doi.org/10.1007/s00769-019-01389-5

GENERAL PAPER

Evaluation of measurement uncertainty in the elemental analysis of sintered silicon carbide using laser ablation in liquid—inductively coupled plasma mass spectrometry with external calibration and isotope dilution

Masahide Fujiwara1 · Koki Hirosawa1 · Naoko Nonose2 · Sho Nishida1 · Naoki Furuta1

Received: 28 November 2017 / Accepted: 25 April 2019 / Published online: 3 June 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019

AbstractThe goal of this study was to evaluate the uncertainty of elemental analytical methods that use laser ablation in liquid (LAL) as a pretreatment. After LAL sampling of silicon carbide (SiC), trace impurities were quantified using inductively coupled plasma-sector field mass spectrometry (ICP-SFMS) with external calibration (EC). The expanded uncertainty (k = 2) of the concentrations was less than 10 %. To obtain more precise values, the Ti, the element homogeneously distributed on the sample surface of SiC, was quantified using ICP-SFMS with isotope dilution mass spectrometry (IDMS). The expanded uncertainty (k = 2) was reduced to 3.4 %. The smaller uncertainty associated with IDMS reflected the fact that measuring the isotope ratio of the same element with IDMS and high-speed isotope measurements at 10-ms intervals reduced the vari-ability of signal intensities, the primary source of uncertainty, more effectively than EC. Moreover, the combination with ID improved the sample amount-dependent unrepeatability in pretreatment.

Graphical abstract

Extended author information available on the last page of the article

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Keywords Silicon carbide · Laser ablation in liquid · Isotope dilution mass spectrometry · External calibration · Uncertainty evaluation · ICP sector field mass spectrometry

Introduction

Silicon carbide (SiC) has unique physical and chemi-cal properties, including a wide band gap, high dielectric breakdown field strength, high thermal conductivity, and high chemical resistance. Because of these properties, SiC has been widely used in a variety of industrial applications (e.g., semiconductors, grinding materials, and nuclear reac-tors) [1]. Because trace amounts of impurities affect these SiC properties, it is necessary to determine the concentra-tions of impurities in the materials [2]. Inductively coupled plasma mass spectrometry (ICPMS) has been widely used as a highly sensitive multi-element analytical method. It is generally necessary to convert a solid sample into a solution by acid digestion prior to an ICPMS measurement. How-ever, because SiC is highly refractory, decomposing SiC by acid digestion, a typical pretreatment method for elemental analysis, is difficult [3].

Recently, Machida et al. [4] have reported that laser abla-tion in liquid (LAL) is a useful pretreatment method for SiC. LAL is used to produce nanoparticles by irradiating the sur-face of a solid sample through a liquid with a laser. They found that pretreatment with LAL changes a bulk sample into many 200-nm-size particles and increases the spe-cific surface area of the SiC. In addition, they revealed that LAL pretreatment converts some SiC chemical structures to Si and amorphous C via melting-congelation. These two effects make it possible to decompose SiC by acid digestion. Three other reports have discussed the application of LAL to elemental analysis: determination of trace elements in National Institute of Standards and Technology (NIST) 611 glass standard reference material (SRM) [5]; measurement of isotope ratios of trace elements in NIST 610 glass SRM and IRMM-014 high-purity iron certified reference material (CRM) [6]; and investigation of elemental fractionation in different size particles during LAL [7]. However, the uncer-tainty of analytical measurements using LAL for pretreat-ment has not been evaluated. LAL also has the advantage of being compatible with the use of standard addition methods and isotope dilution mass spectrometry (IDMS). However, an analytical method combining LAL and these quantifica-tion methods has not been reported.

The goal of this study was to evaluate the uncertainty of analytical measurements using LAL for pretreatment and to reduce the measurement uncertainty using IDMS, which is a primary analytical method [8]. LAL was used for pretreat-ment of sintered SiC, and the particles obtained via LAL pretreatment were digested with acids. The trace elements in the sintered SiC were quantified with an external calibration

method (EC) using inductively coupled plasma-sector field mass spectrometry (LAL-EC-ICPSFMS), and an uncertainty evaluation was performed. To improve the precision of the result, Ti concentrations and their uncertainty were also determined using LAL-ICPSFMS combined with IDMS (LAL-ID-ICPSFMS).

Experimental

Reagents and chemicals

SiC powder CRM (NMIJ 8002-a, National Metrology Insti-tute of Japan, Ibaraki, Japan) and sintered SiC provided by a SiC equipment manufacturer were used as sample materi-als. SiC powder CRMs (NMIJ 8001-a and NMIJ 8002-a, National Metrology Institute of Japan, Ibaraki, Japan) and glass SRMs (NIST 610, NIST 612 and NIST 614, National Institute of Standards and Technology, Maryland, USA) were used as reference materials for laser ablation (LA)-ICP quadrupole (Q) MS. Ultrapure water (> 18.2 MΩ cm, Milli-Q, Merck Millipore, Molsheim, France), HF (50 %, Daikin Industries, Osaka, Japan), HNO3 (EL, 70 %, Kanto Chemical Co., Tokyo, Japan), and H2SO4 (AA-100, 96 %, Kanto Chemical Co., Tokyo, Japan) were used for sample preparation.

The calibration standard solutions for LAL-EC-ICPMS were prepared from single-element standards of Sc, Zr, and La (Kanto Chemical Co., Tokyo, Japan) and a multi-ele-ment standard (XSTC-22, SPEX CertiPrep, Metuchen, NJ, USA) containing Al, Ti, Cr, Mn, Fe, Ni, and Mo. 45Sc was used as an internal standard. These standards were mixed and diluted with 0.1 M HNO3 to make calibration stand-ards of 0 µg kg−1, 0.025 µg kg−1, 0.05 µg kg−1, 0.1 µg kg−1, 0.25 µg kg−1, 0.5 µg kg−1, 1 µg kg−1, 2.5 µg kg−1, 5 µg kg−1, 10 µg kg−1, 25 µg kg−1, 50 µg kg−1, and 100 µg kg−1. Five values of the standards were chosen for each element; the measured values were always near the centroid of the cali-bration curves.

A 49Ti-enriched spike solution for LAL-ID-ICPS-FMS was prepared by dissolving 49Ti-enriched Ti metal (1.33 % ± 0.05  % 46Ti, 1.25 % ± 0.05  % 47Ti, 14.09 % ± 0.10 % 48Ti, 81.61 % ± 0.10 % 49Ti, and 1.73 % ± 0.05 % 50Ti; Oak Ridge National Laboratory, TN, USA) in HNO3. A trace amount of HF was added to the 49Ti spike solution for stabilization of Ti in HNO3 [9]. The concentration of the 49Ti spike solution was determined by reverse isotope dilu-tion analysis based on the concentration of the Ti standard solution (SPEX CertiPrep).

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Instrumentation

ALA system (UP213, Elemental Scientific Laser, Boze-man, MT, USA) was used in this study. An ICP-SFMS instrument (Element XR, Thermo Fisher Scientific Inc., Bremen, Germany) was used for comparison of uncer-tainties of LAL-EC-ICPSFMS and LAL-ID-ICPSFMS in the elemental analysis of a sintered SiC surface, and an ICPQMS instrument (7500ce, Agilent Technologies, Tokyo, Japan) was used for evaluation of element homo-geneity on a sintered SiC surface by LA-ICPQMS. The ICP-SFMS measurements were performed in a medium-resolution mode (m/Δm = 4000) to prevent interference of 49Ti from polyatomic ions (32S17O, 33S16O) derived from H2SO4 in the IDMS and interference from Ar-associated polyatomic ions in the EC.

A microwave digester (ETHOS ONE, Milestone, Socisole, Italy), polytetrafluoroethylene (PTFE) vessel (HPV-100, Milestone), and perfluoroalkoxy (PFA) vial (F-100-42, Flon Industry, Tokyo, Japan) were used for acid digestion of SiC powder CRM and sintered SiC. A micro-balance (MSA6.6S-000-DM, Sartorius, Gӧttingen, Ger-many) was used to determine the amount of sintered SiC sampled by LAL. A particle size analyzer (ELSZ-2000, Otsuka Electronics, Osaka, Japan) with dynamic laser scattering (DLS) was used to measure the particle size distribution of sintered SiC particles generated by LAL.

Procedures for LAL sampling

An open-top chamber made of PFA was used for LAL sampling [7]. The outer diameter, inner diameter, and height of the chamber were 36 mm, 32 mm, and 10 mm, respectively. Sintered SiC was placed in the open-top chamber, and then 5.6 mL of ultrapure water was added to the chamber. The surface of the sample was therefore 3 mm below the surface of the water. The 2 × 4 mm2 of sample surface was irradiated with 40 laser lines under the LA conditions shown in Table 1. Ablation with the laser lines took approximately 2.5 h. After ablation, the LAL-sampled particles suspended in the water were transferred to a PFA vial with a micropipette. In addition, 1.4 mL of ultrapure water was added to the chamber and the remained particles were also collected by the same procedures. Total volume of LAL sample was 7 mL, and the LAL sample was subjected to acid digestion. After removing water by blowing, the sintered SiC was weighed five times with a microbalance. The sampled amount of sintered SiC was calculated from the difference between the average weights of the sintered SiC before and after LAL sampling. The amount of sintered SiC sampled was approximately 0.2 mg.

Sample digestion and procedures for solution nebulization EC‑ICPSFMS

Figure 1 summarizes the procedures for analysis of SiC pow-der CRM and sintered SiC via EC. Two milligrams of the SiC powder was weighed with a microbalance, suspended in 3 mL of ultrapure water, and subjected to microwave digestion. The SiC powder suspension was transferred to an 8-mL PFA vial and mixed with 0.1 mL of 96 % H2SO4 to prevent complete dryness in the following evaporation step. The samples were evaporated to a droplet by heating on a hot plate at 200 °C for 1 h. Aliquots of 0.1 mL of 50 % HF, 0.1 mL of 70 % HNO3, and 0.1 mL of 96 % H2SO4 were added to the samples in the PFA vial. The PFA vial was placed in a microwave PTFE vessel, and 2 mL of 50 % HF, 2 mL of 70 % HNO3, and 3 mL of 96 % H2SO4 were added to the vessel [10]. The digestion of LAL-sampled SiC par-ticles was carried out using the same procedures described above for the SiC powder CRM. The digested solutions of the SiC powder CRM and the sintered SiC were transferred to a platinum crucible and dried on a hot plate at 350 °C for 20 min to remove H2SO4, which would otherwise have caused a matrix effect. The resulting dried residues were dissolved in 1 mL of 5 M HNO3 on a hot plate at 150 °C for 15 min. The dissolved samples were diluted to 4 g for SiC CRM and 2 g for sintered SiC with 0.1 M HNO3. Four samples (and two blanks) were prepared for the SiC pow-der CRM and the sintered SiC. The obtained solutions were subjected to ICP-SFMS measurements under the operating conditions indicated in Table 2.

Procedures for isotope dilution analysis

Figure 1 shows the procedures used to analyze the sintered SiC by IDMS. It does not reach isotope equilibrium even if a spike is added before LAL sampling, and the recov-ery of sample pretreatment process cannot be corrected for. Furthermore, if 1 mL of spike solution is added before

Table 1 Operating conditions for laser ablation in liquid (LAL)

Laser ablation system (UP213) LAL LAL-ICPQMS

Laser type Nd:YAG Nd:YAG Wavelength/nm 213 213Pulse width/ns 4 4Laser energy/mJ 0.63 0.54Fluence/J cm−2 8.0 6.8Diameter of crater/μm 100 100Scanning speed/μm s−1 10 10Ablation time/min 147 1Ablation area/mm2 8 0.06Carrier gas flow (He)/L min−1 – 1.0

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acid digestion process, 0.4 mL of acids used for digestion is diluted and the acid digestion cannot be proceeded well. Then, 49Ti spike solutions were added to the digested SiC solutions, which were obtained by the same procedures described in the previous section, as well as to blanks. In accordance with a previous study [11], we adjusted the 47Ti/49Ti ratio to an optimum value (0.4) by adding 1 g of a 5 µg kg−1 49Ti spike solution to four samples and 0.1 g of a 0.5 µg kg−1 49Ti spike solution to two blanks. ICP-SFMS measurements of IDMS were conducted in parallel with reverse IDMS to compensate for the effect of any uncertainty

of the isotopic composition of the spike solution [11]. For the reverse IDMS solution, 5 g of a 500 µg kg−1 49Ti spike solution was mixed with 5 g of a 10 mg kg−1 Ti standard solution so that the 47Ti/49Ti ratio was 0.4. To measure isotope ratios as accurately as possible, IDMS and reverse IDMS were performed under operating conditions such that 47Ti and 49Ti were measured almost simultaneously; the two isotopes were scanned at high speed by shortening the dwell time and setting the settling sampling point to 5. For isotope ratio measurements via IDMS, a bracketing method using the reverse IDMS solution was employed to correct for

Resolve and condensefor 1 droplet

(150 , 15 min)

Evaporation to drynessin a platinum crucible

(350 , 20 min)

SiC standard (2 mg)

Microwave digestion(HNO3, HF, H2SO4, 210 , 1 hour)

Evaporation to drynessin a platinum crucible

(350 , 20 min)

5 M HNO3 1 mL

Resolve and condensefor 1 droplet

(150 , 15 min)

Dilution(2 g)

ICP-SFMS(EC)

<EC-

Evaporation (200 , 2 hours)

LAL sampling(0.2 mg)

Dilution(4 g)

LAL sampling(0.2 mg)

Microwave digestion(HNO3, HF, H2SO4, 210 , 1 hour)

49Ti spike solution5 μg kg-1 1 g

5 M HNO3 1 mL

0.1 M HNO3

Dilution(2 g)

ICP-SFMS(ID)

Evaporation (200 , 2 hours)

<ID-ICPMS>

Evaporation (200 , 1 hour)

200 μg kg-1 Sc 0.1 g(Internal standard)

0.1 M HNO3

400 μg kg-1 Sc 0.1 g(Internal standard)

0.1 M HNO3

ICPMS>

Fig. 1 Procedures used to analyze SiC powder CRM and sintered SiC

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mass discrimination effects [12]. ICP-SFMS measurements were performed under the operating conditions indicated in Table 2.

Procedures for LA‑ICPQMS analysis

For LA-ICPQMS, disk-shaped pellets (diameter, 10 mm; height, 2 mm) were prepared by pressing 300 mg of two SiC powder CRMs at 10 MPa for 60 s. Laser ablation was performed under a He atmosphere. Ablated particles smaller

than 1.0 µm were introduced into an ICPQMS by using a cascade impactor (type NL-1-1A, Tokyo Dylec, Tokyo, Japan). Seventy-two lines (0.6 mm long) around the LAL-sampled area were analyzed by LA-ICPQMS under the oper-ating conditions shown in Tables 1 and 2. Figure 2 shows a photograph of sintered SiC and a schematic of the LA-ICPQMS analysis site. The calibration curves for Al, Ti, Cr, Mn, Fe, Ni, Mo, Y, and La were prepared with SiC CRMs (NMIJ 8001-a and 8002-a); that for Zr was prepared with NIST glass SRMs (610, 612, and 614).

Table 2 Operating conditions for inductively coupled plasma mass spectrometer (ICPMS)

ICPMS EC-ICPSFMS ID-ICPSFMS LA-ICPQMS

ICP operating conditions RF power/W 1250 1250 1550 Plasma gas flow (Ar)/L min−1 16 16 15 Carrier gas flow (Ar)/L min−1 1.105 1.100 1.3 Auxiliary gas flow (Ar)/L min−1 0.85 0.95 1.0 Sampling depth/mm 4.8 3.0 6.5

Measuring conditions Resolution of mass spectrometer/m ∆m−1 4000 4000 300 Dwell time/ms 10 2 1 Sampling points/– 63 5 1 Number of sweeps 3 600 100 Integration time/s 1.9 6.0 0.1 Repetitions/– 5 10 1 Measured isotopes 27Al, 49Ti, 52Cr, 55Mn, 56Fe,

60Ni, 89Y, 90Zr, 95Mo, 139La47Ti, 49Ti 27Al, 49Ti, 52Cr, 55Mn,

56Fe, 60Ni, 89Y, 90Zr, 139La

 Internal standard 45Sc – 29Si

LAL sampling

LA-ICPMS

Fig. 2 Photograph of sintered SiC (left) and a schematic of the LA-ICPQMS analysis site (right)

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Results and discussion

Uncertainty calculation of EC, reverse IDMS, and IDMS

The uncertainty of the value in the EC was calculated fol-lowing the method of Hibbert et al. [13]. In the EC, the sam-ple concentration is calculated using the following equation:

where C is the concentration of the solution sample, m is its mass, I is the signal intensity, and a and b are a slope and an intercept, respectively, of the signal intensity versus the con-centration of calibration standard solution. The subscripts sam , sol , and cal refer to the sample, sample solution, and the average of the calibration curve, respectively. The fol-lowing equation was obtained by using a relation equation between a and b:

The subscript cal refers to the average of the calibration curve. The variances in Eq. (2) are independent. The uncer-tainty u of the function f(x1,x2,…,xn) is a value obtained by combining the standard uncertainty of the independent parameter xi and is defined by the following expression.

By defining � ≡Isol−Ical

a− Ccal , the uncertainty of the sample

concentration in the EC can be calculated with the following equation [13].

where n is the number of calibration curve point, m is the number of measurement, Ci is the concentration at each point i on the calibration curve, and u(Cstd)

Cstd

is the relative standard uncertainty of calibration standard solution. The terms in the right side of Eq. (4) correspond to the repeatability of sam-ples, the uncertainty of calibration, the uncertainty of the

(1)Csam =

(

Isol − b

a

)

⋅

msol

msam

(2)Csam =

(

Isol − Ical

a− Ccal

)

⋅

msol

msam

(3)u2(f ) =∑

(

�f

�xi

)2

u2(

xi)

(4)

�

u�

Csam

�

Csam

�2

=�

RSU for Csam

�2

+

s2

a2

�

1

n+

1

m+

(Isol−Ical)2

a2∑

(Ci−Ccal)2

�

�2

+

�

u�

Cstd

�

Cstd

�2

+

�

u�

msam

�

msam

�2

+

�

u�

msol

�

msol

�2

assay standard, the uncertainty of the weight of sample and the uncertainty of the weight of sample solution in sequence.

The uncertainty of the values in reverse IDMS and IDMS was calculated following the method of Nonose et al. [11]. In the IDMS, the sample and spike concentrations were cal-culated using the following equation:

where A and B are natural abundances of isotopes A and B , respectively, K is a correction coefficient of the measured isotope to correct for the mass discrimination effect, and R is a measured isotopic ratio. The subscript sam indicates a sample, sp is a spike, std is a standard solution, bl is a mix-ture of a sample and a spike, and bl′ is a mixture of a spike and a standard solution. By defining � ≡

Astd−Kbl� R

bl� Bstd

Kbl� R

bl� Bsp−Asp

, the

uncertainty of the spike concentration in the reverse isotope dilution (ID) analysis can be calculated with the following equation.

By defining � ≡KblRblBsp−Asp

Asam−KblRblBsam

, the uncertainty of the sample concentration in the ID analysis can be calculated with the following equation.

The terms in the right side of Eq. (7) correspond to the repeatability of the reverse ID blends, the uncertainty due to the atom percent of the assay standard, the uncertainty of the assay standard, the uncertainty of the weight of the spike solution, and the uncertainty of the weight of the assay

(5)Csam = Csp ⋅

msp

msam

⋅

KblRblBsp − Asp

Asam − KblRblBsam

(6)Csp = Cstd ⋅mstd

msp

⋅

Astd − Kbl

�Rbl

�Bstd

Kbl

�Rbl

�Bsp − Asp

(7)

(

u(

Csp

)

Csp

)2

=(

RSU for Csp

)2

+

(

1

Kbl� R

bl� Bsp−Asp

u(

Astd

)

)2

+

(

−Kbl� R

bl�

Kbl� R

bl� Bsp−Asp

u(

Bstd

)

)2

�2

+

(

u(

Cstd

)

Cstd

)2

+

(

u(

msp

)

msp

)2

+

(

u(

mstd

)

mstd

)2

(8)

(

u(

Csam

)

Csam

)2

=(

RSU for Csam

)2

+

(

−(

KblRblBsp−Asp)

(Asam−KblRblBsam)2 u

(

Asam

)

)2

+

(

KblRbl

(

KblRblBsp−Asp)

(Asam−KblRblBsam)2 u

(

Bsam

)

)2

�2

+

(

u(

Csp

)

Csp

)2

+

(

u(

msam

)

msam

)2

+

(

u(

msp

)

msp

)2

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standard solution in sequence; the terms in the right side of Eq. (8) correspond to the repeatability of the ID blends, the uncertainty due to the atom percent of the sample, the uncertainty of the spike concentration, the uncertainty of the weight of the sample, and the uncertainty of the weight of the spike solution in sequence. When reverse ID analysis and ID analysis are performed at the same time, the uncertainty derived from the spike is canceled [11]. Therefore, we did not consider uncertainty derived from spikes in this study. In the ID analysis, it is necessary to prepare an optimal meas-urement isotopic ratio to obtain as accurate results as pos-sible. The uncertainty of the sample concentration derived from the uncertainty of the measurement isotope ratio is expressed by the following equation.

Considering the signal uncertainty of the ICPMS, the uncertainty of the measured isotope ratio is calculated with the following equation:

where Il and Ih are the smaller and the larger signals of the ICPMS, respectively, and k is a constant value that depends on ICPMS conditions. By substituting Eq. (10) into Eq. (9), the uncertainty of the sample concentration due to the uncer-tainty of the signal intensity of the ICPMS is expressed as follows.

(9)

(

u(

Csam

)

Csam

)

R

=R(

BspAsam − AspBsam

)

(

Asam − RBsam

)(

RBsp − Asp

) ⋅

u(R)

R

(10)u(R)

R= k

√

1

Il+

1

Ih= k

√

1

Ih

(

1 +1

R

)

(R ≤ 1)

(11)

(

u(

Csam

)

Csam

)

R

= kR(

BspAsam − AspBsam

)

(

Asam − RBsam

)(

RBsp − Asp

)

√

1

Ih

(

1 +1

R

)

(R ≤ 1)

The optimum R (47Ti/49Ti) at which the uncertainty of the sample concentration derived from the measurement of iso-tope ratio is the smallest is 0.4. In this study, addition of a spike caused the isotope ratio to become 0.4. However, if the R had been calculated from the error magnification factor without considering the signal uncertainty of the ICPMS, the value of R would have been 0.15.

In the ICPMS measurement of this experiment, dead time correction was carried out according to the method of Non-ose et al. [11]. It is known that the uncertainty of dead time can be neglected by matching the isotope ratio in reverse IDMS with that in IDMS. Actually, the relative standard uncertainty of the sample concentrations derived from the dead time correction was 0.1 %. Therefore, the uncertainty of dead time was neglected. The uncertainties of the weights in the EC and IDMS were calculated from the reproducibil-ity of the microbalance measurement.

Validation of sample digestion and ICP‑SFMS measurements

To validate the sample digestion method and ICP-SFMS analyses, SiC powder CRM was subjected to acid digestion, and then an ICP-SFMS analysis was performed. Table 3 shows the concentrations and uncertainties of trace elements in the SiC powder CRM determined by EC-ICPSFMS. The repeatability of four samples, the uncertainty of calibration, and the uncertainty of the assay standard in Table 3 corre-spond to the first, second, and third terms in Eq. (4), respec-tively. The uncertainties of the weight of sample solution were neglected, because the weight was big enough.

The greatest source of uncertainty in EC-ICPSFMS for the SiC powder CRM was the repeatability of the four samples ((1) in Table 3). These results confirmed that the

Table 3 Quantitative results and uncertainties for NMIJ 8002-a analyzed via external calibration (EC) ICPMS

Al Ti Cr Mn Fe Ni Y Mo La

Certified (k = 2)/mg kg−1 189 ± 19 47.7 ± 3.0 61.9 ± 9.4 1.60 ± 0.34 130 ± 7 4.43 ± 0.80 0.58 ± 0.07 109 ± 14 0.37 ± 0.10Analytical result (k = 2)/

mg kg−1199 ± 7 44.1 ± 0.9 68.6 ± 3.0 1.37 ± 0.08 130 ± 4 4.70 ± 0.32 0.500 ± 0.010 87.8 ± 5.9 0.280 ± 0.008

Uncertainty evaluation/relative % Standard uncertainty  (1) Repeatability of 4

samples1.6 0.80 1.9 2.8 1.2 3.3 0.84 2.7 1.2

  (2) Uncertainty of calibra-tion

0.54 0.56 1.2 1.2 0.87 0.39 0.40 1.9 0.67

  (3) Uncertainty of assay standard

0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.20

 Combined uncertainty  [combination of (1), (2) and

(3)]

1.7 1.0 2.2 3.0 1.5 3.4 1.0 3.4 1.4

 Expanded uncertainty (k = 2) 3.4 2.0 4.4 6.1 3.0 6.8 1.9 6.7 2.7

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concentrations of all elements except Mo were consistent with the certified values within uncertainty. To clarify the reason why the concentration of Mo was smaller than the certified value, a Mo standard solution (50 µg kg−1), pre-treated in the same way, was analyzed via ICPQMS. The calculated concentration of Mo was 44 µg kg−1, an 88 % recovery rate. We concluded that the recovery of Mo by HNO3 was probably insufficient and that some Mo remained in the platinum crucible. Therefore, the acid digestion and ICP-SFMS measurement were validated, except for Mo.

Confirmation of digestion of sintered SiC particles generated by LAL

The particle size distribution and digestion of sintered SiC particles generated by LAL were confirmed by a particle size analyzer using DLS. Figure 3 shows the particle size distri-bution of the sintered SiC particles before acid digestion. LAL sampling of sintered SiC generated nanoparticles with average diameters of 124 nm. Particles larger than 1 µm were not observed. Figure 4 shows the autocorrelation function of DLS measurements of sintered SiC particles before and after acid digestions and of a blank. Because there was no

difference in the autocorrelation function between sintered SiC particles after decomposition and a blank, SiC particles generated by LAL were confirmed to have been completely decomposed by microwave digestion.

Quantitative determination and evaluation of measurement uncertainty for trace elements in sintered SiC by LAL‑EC‑ICPSFMS

Table 4 summarizes the trace element concentrations and their uncertainties in sintered SiC determined by LAL-EC-ICPSFMS. The repeatability of four samples, the uncertainty of calibration, the uncertainty of the assay standard, and the uncertainty of the weights in Table 4 correspond to the first, second, third, and fourth terms in Eq. (4), respectively. The uncertainty of the weight of sample solution was neglected, because the weight was large enough. The greatest source of uncertainty in LAL-EC-ICPSFMS was the repeatabil-ity of the four samples ((1) in Table 4). The elements were classified into two groups: one for which the repeatability of the four samples was less than 5 % (Al, Ti, Cr, Fe, Ni, and La) and the other for which the repeatability of the four samples was larger than 15 % (Mn, Y, and Zr). There are two possible reasons why the uncertainty was larger than 15 % in the latter group: errors associated with the analyti-cal method (i.e., contamination) and errors associated with sample inhomogeneity. We hypothesized that elements with uncertainties larger than 15 % were not uniformly distributed on the sample surface.

Evaluation of element homogeneity on sintered SiC surfaces by LA‑ICPQMS

We evaluated the homogeneity of sintered SiC surfaces by LA-ICPQMS. To elucidate the reason for the differences of the uncertainties between elements, the homogeneities of the elements in sintered SiC surfaces were evaluated by LA-ICPQMS. Relative concentrations were defined as follows.

where Cj is the elemental concentration for line j and Cave is the average elemental concentration for 72 lines.

The variations of the relative concentrations were evalu-ated by comparing the relative concentrations (Eq. 12) for each element. Figure 5 shows box plots of the relative con-centrations obtained from 72 lines around the LAL-sampled area. The elements Al, Ti, Cr, Fe, Ni, and La were homoge-neously distributed on the sample surface, but Mn, Y, and Zr were not. This classification agrees with that of Table 4. We therefore think that the large uncertainties in Table 4 were caused by the inhomogeneous distributions of elements on

(12)Crel =Cj

Cave

0

10

20

10 100 1000 10000Num

ber d

istri

butio

n (%

)

Particle size (nm)

Fig. 3 Particle size distribution of sintered SiC particles produced by LAL

Time from the start of DLS measurement (μs)

Aut

ocor

rela

tion

func

Fig. 4 Autocorrelation function of DLS measurement of sintered SiC particles before and after acid digestions and blank. , before acid digestion; , after acid digestion; , blank

337Accreditation and Quality Assurance (2019) 24:329–339

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the sintered SiC surface. It therefore appears that LAL-EC-ICPSFMS can perform simultaneous multi-element analy-ses with an expanded uncertainty (k = 2) [14] of less than 10 % for elements that are homogeneously distributed on the sample surface.

Although the elements Al, Ti, Cr, Fe, Ni, and La were homogeneously distributed on the sample surface, the uncertainty in repeatability of four samples tended to be larger in LAL-EC-ICPSFMS (Table 4) than in EC-ICPS-FMS (Table 3). The difference between these methods is the amount of sample (0.2 mg in LAL-EC-ICPSFMS; 2 mg in EC-ICPSFMS), indicating that the lower repeatability in LAL-EC-ICPSFMS is due to the less amount of sample in LAL sampling. Although significant sample loss was not observed during pretreatment with 2 mg SiC powder CRM (Table 3), random sample loss may occur with less amount of sample.

Quantitative determination of Ti in sintered SiC by LAL‑ID‑ICPSFMS

As an impurity in SiC, Ti is known to affect the band gap, because the electron configuration of Ti is similar to that of Si and C [15]. We therefore investigated whether the uncer-tainty of concentrations was reduced by quantitative deter-mination via LAL-ID-ICPSFMS.

Table 5 shows the concentrations and uncertainties of Ti in sintered SiC determined by LAL-ID-ICPSFMS. The uncertainty of the assay standard, the uncertainty due to the atom percent of the assay standard, and the repeatability of the two reverse ID blends in Table 5 correspond to the first, second, and third terms in Eq. (7), respectively; and the uncertainty of weight, the uncertainty due to atom percent of the sample, and the repeatability of the four ID blends in Table 5 correspond to the first, second, and fourth terms in Eq. (8), respectively. The uncertainties of the weight of Ta

ble

4 Q

uant

itativ

e re

sults

and

unc

erta

intie

s for

sint

ered

SiC

ass

ayed

via

LA

L-EC

-IC

PMS

Al

TiC

rM

nFe

Ni

YLa

VZr

Anal

ytic

al re

sult

(k =

2)/m

g kg

−1

531 ±

3516

3 ± 17

41.7

± 3.

20.

30 ±

0.12

130 ±

1330

.3 ±

2.4

5.6 ±

2.1

0.13

7 ± 0.

008

1.68

± 0.

5512

7 ± 46

Unc

erta

inty

eva

luat

ion/

rela

tive

% S

tand

ard

unce

rtai

nty

  (1)

Rep

eata

bilit

y of

4 sa

mpl

es3.

25.

23.

719

4.5

4.0

192.

816

18  (

2) U

ncer

tain

ty o

f cal

ibra

tion

0.58

0.17

1.1

0.73

1.9

0.37

0.38

0.72

0.53

1.0

  (3)

Unc

erta

inty

of a

ssay

stan

dard

0.25

0.25

0.25

0.25

0.25

0.25

0.25

0.20

0.25

0.20

  (4)

Unc

erta

inty

of w

eigh

t0.

350.

350.

350.

350.

350.

350.

350.

350.

350.

35 C

ombi

ned

unce

rtai

nty

  [co

mbi

natio

n of

(1),

(2),

(3) a

nd (4

)]3.

35.

23.

919

4.9

4.0

192.

916

18

 Exp

ande

d un

cert

aint

y (k

= 2)

6.5

107.

739

108.

138

5.8

3236

0

1

2

3

4

5

Al Ti Cr Mn Fe Ni Y La Zr

Rel

ativ

e co

ncen

tratio

n

Fig. 5 Box plot of the relative concentrations of nine elements obtained at 72 lines around the LAL-sampled area. The sample mini-mum, the lower quartile, the median, the upper quartile, and the sam-ple maximum are shown

338 Accreditation and Quality Assurance (2019) 24:329–339

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spike solution and standard solution were neglected because the weight was large enough. Concentrations of Ti deter-mined by LAL-ID-ICPSFMS and LAL-EC-ICPSMS were 162 mg kg−1 ± 6 mg kg−1 (Table 5) and 163 mg kg−1 ± 17 mg kg−1 (Table 4), respectively, and were within the range of expanded uncertainty (k = 2). Expanded uncer-tainties (k = 2) of Ti determined by LAL-ID-ICPSFMS and LAL-EC-ICPSMS were 3.4 % and 10 %, respectively. The expanded uncertainty (k = 2) was reduced by about a factor of 3 by changing the quantitative method from EC to IDMS.

The greatest sources of uncertainty for the LAL-ID-ICPSFMS were the repeatability of the two reverse ID blends and the repeatability of the four ID blends (Table 5). In contrast, the contributions to uncertainty from the standard solution, natural abundance ratio, and weighing were small. The uncertainty of the LAL-ID-ICPMS improved because these sources of uncertainty were smaller than the repeatability of the four samples (Table 4), which was the largest source of uncertainty for the LAL-EC-ICPSFMS. To reduce the variability of sig-nal intensity, the concentration determined by LAL-EC-ICPSFMS was calculated from the 47Ti/45Sc signal inten-sity ratio using 45Sc as an internal standard. In contrast, the concentration determined by LAL-ID-ICPSFMS was calculated from the signal intensity ratio of two isotopes of Ti, 47Ti and 49Ti. The isotope dilution analysis method is a kind of internal standard method, and it is known that the isotope of the analytical element is an excellent internal standard for correcting the mass fractionation effect, the drift, and the matrix effect [16]. Measuring the isotope ratio of the same element with the LAL-ID-ICPSFMS can

reduce the variability of the signal intensities more effec-tively than the internal standard correction using 45Sc. It is generally recognized that the signal intensity of ICPMS varies because of the influence of plasma fluctuations and flicker noise [17]. In LAL-ID-ICPSFMS, accuracy is improved because flicker noise derived from the nebulizer can be smoothed out by high-speed isotope measurements at 10-ms intervals. Moreover, as described above there is concern that the sample amount-dependent unrepeatability occurs in pretreatment. The combination with ID improved the repeatability in pretreatment.

Three factors affect the uncertainty of LAL-EC-ICPS-FMS and LAL-ID-ICPSFMS: the uncertainty of the sample inhomogeneity, the isotope ratio measurement, and the unre-peatability of pretreatment. To obtain more precise values, it will be necessary to reduce the weighing and isotope ratio measurement uncertainties. To reduce the uncertainty of the isotope ratio measurement, we suggest increasing the amount of sample to increase the concentration of the sam-ple in solution and increasing the integration time to reduce the variation of the signal intensity. Moreover, if the sig-nal intensity is sufficient, the signal variations from plasma fluctuation can be canceled out by using a multi-collector-ICPMS, which can measure two isotopes simultaneously. From the fact that the uncertainty of Ti measurement by LAL-ID-ICPSFMS was larger than that of Ti measurement by EC-ICPSFMS, it is likely that the contribution of the sample amount-derived unrepeatability in pretreatment was large. Thus, it is necessary to clarify the cause of the unre-peatability in pretreatment and develop a robust pretreatment method, which is not affected by sample amount, for LAL sampling.

Conclusions

In this study, we could determine the concentrations of multiple elements by LAL-EC-ICPSFMS with an expanded uncertainty (k = 2) of less than 10 % if the elements were homogenously distributed on the sample surface. We believe that larger uncertainties were caused by the inhomo-geneous distribution of some elements on the sintered SiC surface. LAL-EC-ICPSFMS is an analytical method that combines local analytical capability and an accuracy that cannot be obtained by bulk analysis and various direct, solid analytical methods. A comparison of the concentrations of Ti in sintered SiC determined by LAL-EC-ICPSFMS and LAL-ID-ICPSFMS revealed that the expanded uncertainty (k = 2) was reduced by about a factor of 3 by changing the analytical method from EC to IDMS. The advantage of LAL-ID-ICPSFMS compared to LAL-EC-ICPSFMS is higher precision.

Table 5 Quantitative results and uncertainties for sintered SiC assayed via LAL-ID-ICPMS

Analytical result of Ti (k = 2)

162 ± 6 mg kg−1

Uncertainty evaluation/relative % Reverse IDMS  (1) Repeatability of two reverse ID blends 1.1  (2) Uncertainty due to atomic fraction of assay standard 0.24  (3) Uncertainty for assay standard 0.25  (4)) Uncertainty of spike concentration  [combination of (1), (2) and (3)]

1.2

 IDMS  (5) Repeatability of four ID blends 1.2  (6) Uncertainty due to atomic fraction of sample 0.21  (7) Uncertainty of weight 0.35  (8) Uncertainty of sample concentration [combination of

(5), (6) and (7)]1.3

 Combined uncertainty  [combination of (4) and (8)]

1.7

 Expanded uncertainty (k = 2) 3.4

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Acknowledgements This research was supported by the Ministry of Education, Culture, Sports, Science, and Technology, Japan, through a Grant-in-Aid for Scientific Research (C) (No. 17K05909).

Compliance with ethical standards

Conflict of interest The authors declare that they have no conflict of interest.

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Affiliations

Masahide Fujiwara1 · Koki Hirosawa1 · Naoko Nonose2 · Sho Nishida1 · Naoki Furuta1

* Naoki Furuta nfuruta@chem.chuo-u.ac.jp

1 Faculty of Science and Engineering, Department of Applied Chemistry, Chuo University, 1-13-27 Kasuga, Bunkyo, Tokyo 112-8551, Japan

2 National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8563, Japan