Geochemical Journal, Vol. 36, pp. 465 to 473, 2002 238 U/230Th disequilibrium measurement for volcanic standard rock samples using a multiple-collector ICPMS SATORU FUKUDA * and SHUN’ICHI NAKAI Earthquake Research Institute, University of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan (Received November 26, 2001; Accepted April 22, 2002) The radioactive disequilibrium measurements between 238U and 230Th with a Multi-Collector Inductively Coupled Plasma Mass Spectrometer (MC-ICPMS) were applied to igneous standard rocks distributed by Geological Survey of Japan and Geological Survey of the United States. We modified sample dissolution and Th separation method, as well as Th isotope analysis by MC-ICPMS described by Nakai et al. (2001). High sensitivity of our ICP-MS enabled to analyze less than 10 ng Th. The abundances of U and Th were determined by an isotope dilution method, using a 235U depleted uranium reagent and 230Th prepared by milking of natural U as spikes. We can determine 238U/ 232Th abundance ratio with a precision of about 2%. This procedure was applied to ( 238U/230Th) radioactive disequilibrium measurements of igneous standard rock samples. Samples older than 350 Ka were found to attain secular equilibrium, indicating the accuracy of our analysis. On the other hand, young igneous standard rocks were found enriched in 238 U relative to 230 Th, (238U/230Th) activity ratio > 1, which is often observed for igneous rocks from subduction zones. a high first ionization potential (5.95 eV) and is difficult to ionize with the thermal ionization. The isotope analysis of Th by TIMS usually consumes about 100 ng of Th. Since 1990’s, multiple-collector inductively coupled plasma mass spectrometry (MC-ICPMS) has been introduced into the field of isotope geochemistry. The advantage of MC-ICPMS is its high ionization efficiency that enables analysis of elements with a high ionization potential, such as W, Fe and Th (Halliday et al., 1998; Luo et al., 1997). ICP-MS reduced the required amount of Th for determination of its isotope ratio to less than 10 ng (Nakai et al., 2001). In recent radioactive disequilibrium studies, the determinations of U and Th abundances are carried out by isotope dilution analysis. In general, artificially produced nuclides, 229Th and 236U (Turner et al., 1997), or highly enriched 230Th and 235 U (Joannon et al., 1997) are used as spikes. I NTRODUCTION The 230Th is one of the radioactive nuclides in the 238U decay series. The radioactive disequilibrium between 238U and 230Th results from chemical fractionation between U and Th and it returns to equilibrium with a time scale of the half-life of the daughter nuclide. The 230Th has a half-life of 7.52 × 10 4 yr and can be used to investigate the timing of chemical fractionation between U and Th for the time scale of ten to several hundred thousand years. The radioactivity disequilibrium dating has been applied to volcanology, paleoenvironmental studies and archaeology and so on in late Quaternary (Ivanovich and Harmon, 1992). Thermal Ionization Mass Spectrometry (TIMS) has been used for 238U/230Th disequilibrium measurements since 1980’s (Goldstein et al., 1989) and provides the most accurate data. Th, however, has *Corresponding author (e-mail: [email protected]) 465 466 S. Fukuda and S. Nakai These spikes are appropriate for accurate analysis. However, purchase of these materials requires special permission from the government in Japan. Nakai et al. (2001) determined the abundances of U and Th by using an ICP-MS with a quadrupole mass analyzer. They have estimated errors for U/ Th concentration ratio about 5%. The large errors for U/Th concentration ratio give rise to large dating errors. In this study, we prepared moderately enriched 230Th spike from natural U solution, and used a U reagent depleted in 235U as an U spike. We will report the precision of isotope dilution analysis using the in-house prepared spikes and the results of radioactive disequilibrium analysis for standard rock samples distributed by Geological Survey of Japan and by Geological Survey of the United States. EXPERIMENTAL Reagents and samples All experiments were carried out in a clean room under condition of class 1000. Highly purified acids, hydrochloric acid (Kanto, 18078-1B), nitric acid (Kanto, 28163-1B), hydrofluoric acid (Kanto, 18083-1B), and perchloric acid (Kanto, 32059-1B) were used without further purification. Boric acid (Merck, Suprapur) was used as obtained. The water used in this study is 18.3 MΩgrade, which was prepared by a Millipore purification system. Eight standard rock samples distributed by Geological Survey of Japan (Ando and Shibata, 1988) and an AGV-1 distributed by Geological Survey of the United States (Flanagan, 1973) were analyzed for 238U/230Th radioactive disequilibrium measurements. Five samples among nine, JB-1, JA-2, JR-1, JR-2 and AGV-1 are older than 350 Ka and they are expected to attain radioactive equilibrium. Preparation of U and Th spike solution The abundance measurements of U and Th were carried out by isotope dilution analysis. A reagent of depleted U (U(NO3)4, Fluka chemika, 94270), was used as an U spike. The 230Th spike was prepared by separation of 230Th from natural U. This separation method is the same as that used for Th separation from rock samples. The natural U of ca. 50 mg was dissolved in a Teflon beaker with 1 ml of 7N HNO3. This sample solution was loaded onto the column with 1 ml of anion exchange resin (BioRad AGX1-8). The U was eluted with 12.5 ml of 7N HNO3, and the Th was collected with 5 ml of 9N HCl. The 230Th spike solution is treated twice to ensure complete separation from U. The two solutions, depleted U and purified 230Th solution were mixed, and the isotope ratios of 235U/238U and 230Th/232Th and the abundances of U and Th were measured. Isotopic composition of U in the mixed spike was determined by static-multi analysis using a sector ICP-MS, IsoProbe, described later. A mass fractionation correction was made using a natural U solution. Isotopic composition of Th was determined by peak jump analysis using a Daly multiplier with IsoProbe. A mass fractionation correction was also made using a natural U solution. The isotope ratios of 235 U/ 238U and 230Th/ 232Th are 0.002339 ± 0.40% (n = 6, 2σ) and 0.04180 ± 1.6% (n = 10, 2σ ), respectively (Table 1 and Fig. 1). The data whose deviations from the average are larger than 2σ are excluded from calculations. The abundances of U and Th were measured by inverse isotope dilution using standard solutions, whose isotope ratio and abundance were known. The concentrations of U and Th are 2.47 ± 0.44% (n = 5, 2 σ) and 0.0215 ± 0.75% (n = 5, 2σ), respectively. Sample decomposition We modified an analytical scheme described in Nakai et al. (2001). Rock powders of 50 to 100 mg were weighed into screw cap Savillex beakers. Rock samples were digested sequentially by HF (48w%, 1.0 ml)/HClO 4 (30w%, 0.3 ml) and HCl (30w%, 0.5 ml)/H 3BO3 (2.0w%, 0.5 ml). The thorium fluoride that remained after HF/HClO 4 acid attack was dissolved by HCl/H 3BO3 (Turner et al., 1996). The solution was dried down and redissolved with 10 ml of 2w% HNO3, which was completely clear. This HNO3 solution was divided 238 U/ 230Th disequilibrium measurement for volcanic standard rock samples 467 Table 1. Results of U and Th isotopic analysis for spike solution No. [ 2 3 5 U/2 3 8 U] iso to p e ratio * [ 2 3 0 Th/2 3 2 Th] iso to p e ratio * 1 2 3 4 5 6 7 8 9 10 0.0023396 ± 0.0000019 0.0023386 ± 0.0000016 0.0023440 ± 0.0000015 0.0023322 ± 0.0000017 0.0023344 ± 0.0000019 0.0023424 ± 0.0000015 0.04244 ± 0.00034 0.04221 ± 0.00027 0.04189 ± 0.00028 0.04166 ± 0.00038 0.04158 ± 0.00038 0.04134 ± 0.00022 0.04150 ± 0.00030 0.04201 ± 0.00025 0.04184 ± 0.00034 0.04157 ± 0.00027 mean 0.0023386 ± 0.0000091 0.04180 ± 0.00068 (a) *Errors are 2 σ. into two aliquots with weight, one of which is used for isotope dilution analysis and another for isotope ratio measurements, with the proportion of one to four, respectively. More amounts of solutions are required for the isotope ratio measurements. Chemical separation The U and Th in solutions were separated from rock matrix by anion exchange resin (BioRad AGX1-8). We put 1 ml of resin into heat-shrinkable FEP columns with an i.d. of 8 mm, a length of 80 mm and a polyethylene frit. Resin was cleaned with 9N HCl and Milli-Q water sequentially and was conditioned with 7N HNO3. The spiked and un-spiked sample solutions after dissolution were dried and re-dissolved with 1 ml of 7N HNO3 and then loaded on to the resin. Almost all of the elements except U and Th were eluted with 2.5 ml of 7N HNO3. U was then eluted by the addition of 10 ml of 7N HNO3. Finally, Th was collected with 5 ml of 9N HCl. Recovered solutions were dried down and dissolved in 2% HNO3 for ICP analysis. This separation method was calibrated using JB-1 and JB-2. The U and Th fractions from the two samples were analyzed using an ICP-MS with a quadrupole mass analyzer (PQ3, ThermoElemental, Winsford, UK), the recoveries of U and Th were calculated to 80–90%. This separation protocol can handle a sample of (b) Fig. 1. Results of isotopic analysis of spike solution. (a) Results of [235U/238U]isotope ratio. (b) Results of [230Th/ 232 Th]isotope ratio. Errors are 2σ. up to 80 mg. The blanks of U and Th for the total chemical procedure are 40 and 5 pg, respectively, which were determined by measurements using the PQ3. Instrumentation and data correction We used a hexapole-interfaced multiple-collector Inductively Coupled Plasma Mass Spectrometer (IsoProbe, MICROMASS, Manchester, UK) for U and Th isotope dilution analysis and Th isotope measurements. Nakai et al. (2001) described this instrument and a method for mass fractionation correction and only a brief summary is given here. IsoProbe is a multi-collector magnetic sector mass spectrometer with an ICP ion source, and uses a collision cell instead of an energy analyzer. The collision cell is applied to reduce energy spread of ions from the plasma ion source. This instrument is equipped with eight Faraday collectors for the simultaneous acquisition of multiple isotopes. A Daly detector is situated behind the 468 S. Fukuda and S. Nakai axial Faraday. Ions passing onto this collector can be energy filtered using a WARP (Wide Angle Retarding Potential) filter. This filter increases the abundance sensitivity, high enough to cut the tail of large 232Th for 230Th acquisition. The abundance sensitivity is 74 ppb, determined by measuring the contribution of tailing of mass 238 on mass 237 using a uranium standard solution. This abundance sensitivity is high enough for thorium isotope analysis on typical volcanic rock samples (230Th/ 232 Th > 1 × 10–6). Faraday cups and electrometers with 10 11 Ω feed-back resistors were used for acquisition of 232Th, 235U and 238U. The gains of the amplifier associated with each Faraday collector were calibrated with respect to axial Faraday collector. No correction for collector efficiency was made in this study. All measurements were performed with a desolvating nebulizer (Aridus, Cetac, Omaha, Nebraska, USA). Sample uptake rate was about 50 µl/min. A sample solution of 0.6 ml was required for acquisition of 50 ratios including time for stabilizing signals. Measurements of U and Th isotope ratio were performed by a multi-static mode. For U analysis, 234U was measured by a Daly and 235U and 238 U were measured by Faraday collectors. For Th analysis, 230Th and 232Th were measured by a Daly and a Faraday collector, respectively. Mass fractionation introduced by an ICP ion source is about an order of magnitude larger than that of TIMS. In addition, a Daly/Faraday gain factor is required to obtain a thorium isotope ratio. We used our in-house natural U standard for the two corrections. The isotope ratios of 234U/ 238 U and 235U/238U of this natural U standard were assumed to be 0.0000554 and 0.00725, respectively. Mass fractionation for isotope dilution analysis of U was estimated by measuring [ 235U/ 238 U]isotope ratio of the standard solution before and after each sample measurement. For Th isotopic measurements, mass fractionation corrected [234U/ 238 U]isotope ratio of the natural U standard solution was used to determine a relative Daly-Faraday gain factor. In addition, mass fractionation effect for Th was corrected by measuring [ 235 U/ 238 U]isotope ratio of the standard solution before and after each sample measurement. It is known that a mass bias factor of ICP-MS depends on mass number of the nuclides to be analyzed, and elements of similar atomic mass number exhibit similar mass bias factor (Hirata, 1996). Therefore, we can make a mass fractionation correction for Th isotope measurement using the factor determined by the U standard. RESULTS AND DISCUSSION Measurement of U isotope ratio We routinely measured [235 U/ 238U] isotope ratio and [ 234U/238U] isotope ratio of a 30 ppb natural U standard solution for mass fractionation correction and to determine Daly/Faraday gain factor. The 30 ppb standard solution gave about 4.5 × 10 –11 A signal for 238U. Repeated analysis during a day gave the results for [235U/238U]isotope ratio and [234U/238U]isotope ratio of 0.007173 ± 0.12%(2 σ ), 0.0000437 ± 2.4%(2 σ ), respectively. Mass fractionation and Daly/Faraday Gain factor corrections were made using the results of the U standard solution before and after a sample measurement. The variations of the two ratios adjacent to measurements were smaller than the variations during whole day. When the variation was large, the data was rejected and the sample was re-analyzed. Fig. 2. Results of Th isotopic analysis of a standard rock JR-1. Each symbols, 䉬, 䊐, 䉱, 䉫 and 䊏 show the results for 1 ppb, 5 ppb, 10 ppb, 30 ppb and 50 ppb, respectively. Error for each analysis and mean are 2σ and 2 σmean, respectively. 238 U/ 230Th disequilibrium measurement for volcanic standard rock samples Measurement of Th isotope ratio A 50 ppb solution was usually used for Th isotope analysis. This concentration gave about 8.0 × 10–11 A for 232Th, 1.1 × 10–16 –3.2 × 10–16 A for 230 Th. The background for the mass number of 230 was about 1.6 × 10–18–3.2 × 10–18 A, and counted before measurements for 60 seconds and it was subtracted from the intensity of 230Th of a sample. Fifty ratios of [232Th/230Th]isotope ratio were acquired in 12 minutes that consume 30 ng of Th. Table 2 and Fig. 2 show the results of [ 232Th/ 230 Th]isotope ratio analysis for JR-1 solutions with different concentrations. Internal precision of an individual measurement and repeatability for 50 ppb solution within a day is about 0.3% and 0.5%, respectively. We analyzed 1, 5, 10 and 30 ppb solutions as well, to investigate the required Th concentration for accurate analysis. The error associated with the mean values for each concentration was 2σ. The results from 5, 10 and 30 ppb analysis were consistent with that for the 50 ppb solution although internal precision and repeatability were slightly deteriorated. The precision of 1 ppb analysis is low due to weak 230Th signal compared with the background. This indicates that we can reduce the concentration of sample solution down to 5 ppb, thus we can measure [232Th/230Th]isotope ratio using 3 ng Th. The Th isotope ratios of JB-1 and AGV-1 (Table 4) are in good agreements with the TIMS measurement by Reid and Ramos (1996), confirming the accuracy of the present method. The precision of isotope dilution analysis The precision of abundance determinations by isotope dilution method is influenced by an enrichment factor of the spike and spike to sample ratio. The relation between precision of an abundance determination (|dC/C|) with that of an isotope ratio measurement (|dR/R|) is described by Table 2. Results of Th isotopic analysis for a standard rock JR-1 No. Intensity of 2 3 2 Th (×10– 1 1 A) [ 2 3 2 Th/2 3 0 Th] iso to p e ratio * 50 ppb 1 2 3 mean 5.73 5.90 5.91 183900 ± 600 184700 ± 700 184700 ± 600 184400 ± 920 30 ppb 1 2 3 mean 3.66 3.74 3.79 184500 ± 700 184600 ± 800 185000 ± 800 184700 ± 530 10 ppb 1 2 3 4 mean 1.35 1.26 1.28 1.38 184300 ± 1300 184200 ± 1000 186100 ± 800 185500 ± 1400 185000 ± 1860 5 ppb 1 2 3 4 mean 0.68 0.67 0.67 0.70 186100 ± 2000 185800 ± 1900 184000 ± 1800 185700 ± 1600 185400 ± 1900 1 ppb 1 2 3 mean 0.15 0.16 0.15 184900 ± 4100 183500 ± 3600 185400 ± 3400 184600 ± 2000 Th concentration *Errors are 2 σ. 469 470 S. Fukuda and S. Nakai the following equation (Colby et al., 1981). dC dR =F C R (1) where F is an error multiplication factor. When enriched 235U or artificially produced 236U is used as a spike, the F value is close to unity. However, in Japan, permission from the government is required to handle these U spikes. The F value, when depleted U is used as a spike, is larger than that when an enriched isotope or an artificially produced isotope is used. The F value can be theoretically calculated by the following equation: F= ( Rsp − Rn )R . ( R − Rn )( Rsp − R) (2 ) In the case of U, Rn is [235U/ 238U]isotope ratio of the sample, Rsp is [235U/238U] isotope ratio of our spike, respectively, and R is [235U/ 238U] isotope ratio of a spike-sample mixed solution. The F value changes according to the proportion of sample and spike in the mixture. The analysis of our in-house spike solution is optimized when the Ms/Mn value is 1.75, where Mn and Ms are amounts of uranium for sample and spike in the mixture, respectively. The F value then is still rather large around 3.6. On the other hand, the F values of Th isotope dilution using our in-house spike solution are closer to unity for large range of the Ms/Mn from 0.001 to 0.1. The errors for quantitative analysis by isotope dilution are estimated from the value F and precision of isotope analyses. The results of five analyses on JB-2 are shown in Table 3. The F value for U is large, and that for Th is small. On the other hand, the precision of [235U/238U]isotope ratio measurements is better than that of [232Th/230Th] isotope ratio measurements. This is due to instability of Daly/Faraday Gain factor. Accordingly, the error for U determination is similar to that of Th. For precise measurements, the amount of spike to be added to a sample is important. We estimated the concentration of uranium in samples by using an ICP-MS PQ3 prior to the dilution analyses. In Table 3, each error associated with U and Th abundances was calculated with Eq. (1). The errors associated with mean values of U and Th abundances and U/Th abundance ratio were 2 σ. The error of the mean value of U abundance is more than three times of errors associated with each measurement. The errors of the mean values for Th and U/Th abundance ratio are comparable to that of each measurement. The reproducibility of our analytical method can be estimated by the experiments on JB-2 and the error of ( 238 U/ 232 Th)activity ratio was estimated to be less than 2.3%, although we cannot evaluate if the problem of sample heterogeneity may reduce the repeatability. The error of (230Th/232Th)activity ratios was estimated as 0.5–2% by the stability of the Daly/Faraday Gain factor from measurements of the natural uranium standard solution before and after sample analysis. Table 3. The results of JB-2 analysis by isotope dilution *Ms/Mn is the ratio of spike (Ms) and sample (Mn) in mixed solution. **Errors are 2σ . 238 U/ 230Th disequilibrium measurement for volcanic standard rock samples 238 U/230Th measurement results from standard rock samples Nine geological standard samples were analyzed for 238U/230Th disequilibrium measurements. The results are shown in Table 4 and Fig. 3. The radioactivity ratios were calculated from isotopic abundances with the following decay constants, λ 230 Th = 9.195 × 10–6 yr–1 (Cheng et al., 2000), λ 232 Th = 4.933 × 10 –11 yr –1 , λ 238 U = 1.551 × 10–10 yr –1 (Firestone, 1999). The radioactive disequilibrium between 238U and 230Th results from chemical fractionation between U and Th. The radioactive disequilibrium will return to secular equilibrium by 350 Ka after the fractionation. Thus, the volcanic rock sample whose eruption time is more than 350 Ka, is expected to attain secular equilibrium, whether or not it had attained disequilibrium at the eruption time. The volcanic rocks in secular equilibrium should have equal ( 238 U/ 232 Th) activity ratio and ( 230 Th/ 232Th) activity ratio in a ( 230 Th/ 232 Th) activity 238 U/ 232Th)activity ratio diagram such as ratios versus ( Fig. 3. They should fall on a line with a slope of unity, called the “equiline” (Dickin, 1995). Table 4. Results of U (ppm) 238 471 The eruption ages of nine geological standard samples are also shown in Table 3. The eruption ages of AGV-1 and JA-1 have not been reported. However, the K-Ar ages of andesite samples from Guano Valley, Oregon, USA, where AGV-1 was collected, was dated to be 14–17 Ma (Sawlan et al., 1995). The age of andesite, which was collected from the same lava as JA-1, was similarly determined by the K-Ar dating method and found to be 180–270 Ka (Hirata, 1999). Four of the nine samples, JA-2, JB-1, JR-1, JR-2 are older than 350 Ka and they should attain radioactivity equilibrium between 230Th and 238U. Reid (1995) in addition, reported that AGV-1 attained radioactive equilibrium, when analysed using TIMS. Thus, these five samples should be plotted on the equiline in Fig. 3. In the results obtained, these samples are plotted on the equiline within the error range. The data of first analysis on JA-2 did not fall on this line. It is likely that thorium fluoride was not decomposed thoroughly before spike addition and resulted in the deviation. The data for JA-2, treated with HCl/H3BO3 after HF/HClO4 attack, plotted well on the equi- U/230 Th analysis for nine standard rocks Th (ppm) ( 2 3 8 U/2 3 2 Th) activ ity ratio * [ 2 3 2 Th/2 3 0 Th] iso to p e ratio ** ( 2 3 0 Th/2 3 2 Th) activ ity ratio 6.29 4.88 9.16 26.5 31.7 0.966 1.438 0.577 1.017 1.052 201500 ± 2820 133200 ± 1680 338100 ± 4730 180600 ± 1440 172000 ± 880 0.925 ± 0.013 1.398 ± 0.018 0.558 ± 0.008 1.032 ± 0.008 1.083 ± 0.006 —a) 14.1 Ma b ) 7.59 Ma b ) 0.81 Ma b ) 0.60 Ma b ) 0.74 3.17 0.22 1.27 1.504 0.980 1.896 1.159 136700 ± 450 200800 ± 2100 152900 ± 1960 174700 ± 2880 1.363 ± 0.004 0.928 ± 0.010 1.219 ± 0.016 1.067 ± 0.018 0.18-0.27 Ma c) 1783d ) 1950-1951d ) 864d ) 133000 ± 2020 1.402 ± 0.021 14.1 Ma b ) Eruption age *** equilibrium samples AGV-1 JA-2 JB-1 JR-1 JR-2 1.94 2.25 1.69 8.64 10.7 disequilibrium samples JA-1 JA-3 JB-2 JB-3 0.35 1.00 0.16 0.47 equilibrium sample (without HCl/H3 BO3 treatment) JA-2 2.39 4.95 1.509 *Errors for (238U/ 232Th) ratio are estimated as 2.3% (2σ ) from five analysis of JB-2. **Isotope ratio. Reid and Ramos (1996) reported 232Th/ 230Th ratio of JB-1 and AGV-1 measured by TIMS, 337090 ± 2.2% (n = 3) and 202150 ± 1.2% (n = 3), respectively. ***References; a) Sawlan et al. (1995) and Reid (1995), b) Uchiumi et al. (1989), c) Hirata (1999), d) Ando and Shibata (1988). 472 S. Fukuda and S. Nakai Fig. 3. (230Th/ 232Th) versus (238U/232 Th) diagram for nine standard rock samples analyzed in this study. The bold line is the equiline (see text). The five samples older than 350 Ka (filled circles) are plotted on the equiline. The open circle is JA-2 data which was not treated with HCl/H3BO 3. The other four samples younger than 350 Ka (open square) were plotted to the right of the equiline. librium line. In following analyses, we used HCl/ H3BO3 attacks for ( 238U/230Th) activity ratio measurements. The accuracy of our analysis was proved, by that the five rock samples older than 350 Ka attained secular equilibrium in Fig. 3. Four samples, JA-1, JA-3, JB-2 and JB-3 are younger than 350 Ka. These samples are the products of island arc volcanisms. It has been reported that young volcanic rocks from island arcs have radioactive disequilibrium between 238 U and 230 Th. In many cases, they are enriched in 238U relative to 230Th, (238U/230Th)activity ratio > 1 (Turner et al., 2000). The disequilibrium was considered to result from the following process. Island arc volcanisms are triggered by addition of fluids from subducting slab and overlying sediment, which lowers the solidus temperature of wedge mantle. The release of the fluids results in enrichment of U since it is more soluble relative to Th. Four young standard rock samples analyzed here have similar characteristic to the study of other arcs. The chronological significance of the disequilibrium of the samples will be discussed in coming report. CONCLUDING REMARKS We have developed a technique for the (238U/ 230 Th) activity ratio measurements for volcanic rock samples using a MC-ICPMS. The required amount of Th for isotope ratio measurement was reduced to 3 ng. The abundances of U and Th were analyzed by isotope dilution using in-house prepared spike solution. The error for U/Th concentration ratio is estimated at about 2%. The accuracy of this measurement method was certified by the results of the analysis on the standard rock samples that should attain radioactive equilibrium. Acknowledgments—We are grateful to Prof. Setsuya Nakada for supporting this work. We thank Dr. Zenon Palacz for advice on analysis. We would like to thank Dr. Yu Vin Sahoo, Dr. Keiji Misawa and Dr. Noriko Kita for improving this paper. Thanks are due to Prof. Ichiro Kaneoka, Dr. Kozo Uto and Dr. Yukiko Hirata for information of eruption ages to igneous standard rock samples, and due to Dr. Sarat Kumar Sahoo for information of decay constants. 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