Patent Publication Number: US-2006008916-A1

Title: Method for measuring strontium isotope ratios using mass spectrometer

Description:
FIELD OF THE INVENTION  
      The invention relates to strontium isotope mass spectrometry and isotope geochronology.  
     BACKGROUND AND PRIOR ART  
      Strontium has four naturally occurring isotopes,  84 Sr,  86 Sr,  87 Sr and  88 Sr all of them are stable. Their isotope abundances are approximately 0.56 percent, 9.86 percent, 7.02 percent and 82.56 percent respectively. The isotopic abundances of strontium are variable because of the formation of the radiogenic  87 Sr by the β −  decay of naturally occurring  87 Rb. For this reason precise isotopic composition of strontium in a rock or mineral that contains rubidium depends on the age and Rb/Sr ratio of that rock or mineral. Generally the ratio  87 Sr/ 86 Sr is used to express relative abundance of strontium in geochronology. Accurately measuring the ratio  87 Sr/ 86 Sr and the concentration of strontium in a rock or mineral can be used to determine the age of that rock or mineral. Because of the concentration of strontium in geology samples is very low, the isotope ratio and concentration of strontium are determined by undiluted and diluted isotope analysis both of them include chemical analysis and mass spectrometric analysis. The method of isotope dilution analysis of strontium has been existed. It based on the determination of isotope composition of strontium in a mixture of a known quantity of “spike” with unknown quantity of sample strontium. The spike of strontium is a solution contains known concentration and known isotope composition of which  84 S is enriched and here  84 Sr/ 86 Sr═S 1 ,  88 Sr/ 86 S═S 2  and  87 Sr/ 86 S═Si. Two of the naturally occurring isotope ratios in a sample are known as constants  84 Sr/ 86 Sr═N 1  and  87 Sr/ 86 Sr═N 2  where N 1 =0.056 584and N 2 =8.37521,  
      There are two ways to determine the isotope ratios and the concentration of strontium in a rock or mineral: 
      1. A conventional way of dating a rock or mineral with a multi-collector mass spectrometric isotope dilution technique involves two procedures: an undiluted run, by which the naturally occurring isotope ratio  87 Sr/ 86 Sr of the sample can be measured; a diluted run, by which the concentration of strontium of the sample can be determined. The two procedures are almost the same: both of them involve one chemical analysis and one mass spectrometric isotope analysis. For example the new product of Finnigan Mat company equipped with virtual amplifier which based on the patent U.S. Pat. No. 342,152 measures undiluted isotopes of strontium of a sample with a high precision, but in order to determine the concentration of strontium of the sample another run of a diluted analysis have to be done.     2. A simple way of dating a rock or mineral with multi-collector mass spectrometric isotope dilution technique in which the diluted run and undiluted run are combined together into one as suggested by the inventor in the patent No. ZL97100609 in Chinese. The prior invention is created for measuring both diluted and undiluted isotope analysis of strontium using multi-collector mass spectrometer. The advantages are as follows: it can combine diluted run and undiluted run together into one, so that the measuring procedure can be only one chemical analysis and one mass spectrometric analysis; it perfectly solves the difference of gains and corrects isotope fractionation automatically.    

      Both of the two ways still have some disadvantages.  
      In the first way above, as an example, although the new product of Finnigan Mat company equipped with virtual amplifier which based on the patent U.S. Pat. No. 342,152 solves the problem of “gain calibration” with a “novel method”, but it still has some disadvantages: the gain calibration must be done after at least extra j times virtual jumps between blocks of measurement, where j is the number of channels of the collectors; it can not normalize diluted isotope analysis and therefore for geochronology sample of Sr two procedures must be done: a undiluted run, by which the naturally occurring isotope ratio  87 Sr/ 86 Sr of the sample can be measured; a diluted run, by which the concentration of strontium of the sample can be measured.  
      The second way mentioned above is based on the invention of patent No. ZL97100609N which is suited to a general multi-collector thermal mass spectrometer equipped without virtual amplifier. The peak jumping is done dynamically through changes of magnet field. It also has some disadvantages:  
      1, the field strength changing quickly from one channel to another need a response time and at the same time the reproducibility of the position of peaks is not exactly the same as the peaks jumping backward and forward.  
      2, as the field strength changes, tails of the moving peaks will interfere with the background of the amplifiers.  
      In order to get good result, following every time of peak jumping there must be a waiting time about 2 or 4 seconds, therefore the measuring time is longer.  
     SUMMARY OF THE INVENTION  
      The object of the invention is to improve the isotope analysis of strontium. A novel method for isotope analysis of strontium has been invented here. The method can combine diluted analysis with undiluted analysis of strontium together into one run which makes the analysis procedure of strontium more simplified.  
      In order to reach the object, an improved method for isotope analysis of strontium is created. The isotopes of the mixed sample of normal strontium with spike will be measured by a multi-collector mass spectrometer. The method includes □ 
      A mass spectrometer equipped with no less than five collectors Fj (j=1, 2, . . . , 5) which statically collect the ion beams of mass numbers of the isotopes of strontium, i.e. the ion beams of mass number  84 ,  85 ,  86 ,  87  and  88  are statically collected by the collects F 1 , F 2 , F 3 , F 4  and F 5  respectively;  
      After no less than three times measuring by virtual peak jumping, the readings of different collectors will be as follows respectively: in the first measuring the output voltages of A 1 , A 2 , A 3 , A 4  and A 5  are v1j(j=1, 2, . . . , 5); in the second the output voltages of A 1 , A 2 , A 3 , and A 4  are v2j(j=1, 2, . . . , ); and in the third the output voltages of A 1 , A 2  and A 3  are v3j (j=1, 2,3)  
      Solving simultaneous equations by combining one of the following no less than three equations: 
 
□ 84 Sr/ 86 Sr □n ·□ 88 Sr/ 86 Sr □n □□v 11 ·v 33□ /□v 13 ·v 31□ 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 1 □□v 14 ·v 23□ /□v 13 ·v 24□ 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 2 □□v 23 ·v 32□ /□v 22 ·v 33□ 
 
 with one of the formulas: 
 
 for undiluted analysis: 
 
 88 Sr/ 86 Sr □n=8.37521  
 
 for diluted analysis: 
 
[S 1 —□ 84 Sr/ 86 Sr □n ]/[□ 84 Sr/ 86 Sr □n —N 1 ]□[S 2 —□ 88 Sr/ 86 Sr □n ]/[□ 88 Sr/ 86 Sr □n —N 2 ]
 
 where ( 84 Sr/ 86 Sr □n ,□ 87 Sr/ 86 Sr □n  and □ 88 Sr/ 86 Sr □n  are normalized mixed ratios and they are variables of the equations; S 1 , Si and S 2  denote the known isotope ratios  84 Sr/ 86 Sr□ 87 Sr/ 86 Sr and  88 Sr/ 86 Sr of the spike respectively, N 1  and N 2  denote naturally occurring ratios  84 Sr/ 86 Sr and  88 Sr/ 86 Sr of strontium. 
 
 the solutions of the simultaneous equations will be: 
 
[□ 87 Sr/ 86 Sr □n ] 1 □√{square root over ((V 14 ·V 23 )·K/(V 13 ·V 24 ))}
 
[□ 87 Sr/ 86 Sr □n ] 2 □√{square root over ((V 23 ·V 32 )·K/(V 22 ·V 33 ))}
 
 where K is the value of □ 88 Sr/ 86 Sr □n.  
 
 Two values of □ 87 Sr/ 86 Sr □n  can be obtained in one cycle of scan. The values of □ 84 Sr/ 86 Sr □n  and □ 88 Sr/ 86 Sr □n  can also be solved by solving the simultaneous equations. 
 
      The following formula can be used to correct the contribution of spike to the ratio □ 87 Sr/ 86 Sr □n:  
 
N i □□ 87 Sr/ 86 Sr □n +[□ 87 Sr/ 86 Sr □n −S i ]·□N 1 −□ 84 Sr/ 86 Sr □n □/□□ 84 Sr/ 86 Sr □n −S 1 □
 
 where Ni denotes the isotope ratio □ 87 Sr/ 86 Sr □n  of the sample to which the contribution of the spike has been corrected). 
 
      If the quantity of spike is zero then □ 84 Sr/ 86 Sr □n−&gt;N1 , the second term in correct formula will be zero and the formula still be valid, this kind of zero spike dilution analysis will be called “virtual dilution analysis”.  
      The invention created a method which includes: measuring the output voltage using virtual amplifier; building up equations based on the measured results of every collectors and on the unknown ratios; solving the equations and getting the isotope ratios of the sample. The invented method has many benefits: 1, it is independent of gains of different amplifiers; 2, it eliminates isotope fractionation automatically; and 3, it can correct the contribution of spike to the natural occurring ratio  87 Sr/ 86 Sr of strontium. So that the diluted run and the undiluted run can be combined together into one. All of the benefits make the procedure of measurement simplified and easier to operate and the measured result reliable;  
      in order to make the examiner deeply understand for reaching the object of the invention, some useful examples for implication and their schematic diagrams are listed and show what techniques are adopt and what effects will be get 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  is schematic diagram of an example for the first measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 2  is schematic diagram of example 1 for the second measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 3  is schematic diagram of example 1 for the third measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 4  is schematic diagram of example 1 for the fourth measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 5  is schematic diagram of example 1 for the fifth measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 6  is schematic diagram of example 2 for the second measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer;  
       FIG. 7  is schematic diagram of example 2 for the third measurement of “peak jumping” by the virtual amplifier mounted on a thermal mass spectrometer; 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT  
      The following examples describe the practices of the invention in detail but they are not used to limit the invention.  
      The invention can be implicated to a thermal mass spectrometer equipped with virtual amplifier. For measuring dilution isotopes of strontium a new Finnigam Mat thermal mass spectrometer, Triton T 1 , is selected in the examples. The virtual amplifier based on the invention of U.S. Pat. No. 342,152 and mounted on the mass spectrometer Triton T 1  includes nine cups F 1 , F 2  . . . F 9  and nine amplifiers A 1 ,A 2  . . . A 9 . The gains of the amplifiers are G(j) (j=1, 2, . . . 9). In the examples of the invention only five cups Fj(j=1, 2, . . . , 5) and five amplifiers Aj (J=1, 2, . . . , 5) are used as shown in  FIG. 1 . The important point is that the ion beams of the isotopes of strontium should keep stable and being collected by five cups statically and correspondingly. In order to complete one cycle of scan and read out the signals of isotope of strontium from the cups in every integrating time ti, a quintuple amplifier is connected to a quintuple cup dynamically and respectively by a relay matrix R 1  (a virtual amplifier is composed in this way). The ratios and concentration of strontium can be obtained in every cycle of scan. The operating is detailed as follows:  
      Adjusting the magnet field and the collectors so that the ion beams of  84 Sr,  (85 Rb)  86 Sr,  87 Sr and  88 Sr of diluted or undiluted sample of strontium are collected statically by the collectors Fj (j=1, 2, . . . , 5) through peak centering technique and supposing that the amplified ion beams are  84 I,  85 I  86 I,  87 I and  88 I respectively. As shown in  FIG. 1 , a virtual amplifier is composed of a quintuple amplifier Aj (j=1, 2, . . . , 5) which is connected to a quintuple cup Fj(j=1, 2, . . . , 5) through a relay matrix R 1 . The controlling of the relay matrix by the software of the mass spectrometer is not belong to the invention and should not be described here.  
     EXAMPLE 1  
      As shown in  FIG. 1  to  FIG. 5 , there are five integrating times ti (i=1, 2, . . . , 5) in one cycle of scan (although in the invention, the integrating times can be three as ti (i=1, t 2 , t 3 ). In order to describe easily, we suppose that the outputs of amplifiers A 1 , A 2 , A 3 , A 4  and A 5  are vij. and the gains of them are G(j) (j=1, 2, . . . , 5) respectively.  
      The figures from  FIG. 1  to  FIG. 5  show the “peak jumping” schematic diagrams of the first example for practicing the invention. The figures include five times integrating t 1  to t 5  which just compose a procedure of a full rotate cycle of scan of a thermal ionization mass spectrometer equipped with virtual amplifier. Under the controlling of the rely matrix, the outputs of the amplifiers G(j) are corresponding to the signals of  84 Sr,  5 Rb,  86 Sr,  87 Sr and  88 Sr in turn in a full rotated scan. The integrated results can be filled in the following table which is a spectrum table of one full rotated peak jumping cycle of scan.  
                              Spectrum Table       of One Quintuple Collector of 5-Virtual Peak Jumping Scan                                                 V 1     V 2     V 3     V 4     V 5                         t1   84   85   86   87   88           t2   85   86   87   88   84           t3   86   87   88   84   85           t4   87   88   84   85   86           t5   88   84   85   86   87                         V 1 , V, 3  . . . V 5  are the outputs of amplifiers A 1 , A 2 , . . . A 5  respectively                t 1 , t 2  . . . t 5  are integrated times of every peak jumping from t1 to t5 respectively.                The numbers in the table represent the intensities of integrated signals corresponding to the mass numbers.             
 
 The table can be expressed as a matrix [vij]:  
             Spectrum   ⁢           ⁢   Matrix                          v   11           v   12           v   13           v   14           v   15               v   21           v   22           v   23           v   24           v   25               v   31           v   32           v   33           v   34           v   35               v   41           v   42           v   43           v   44           v   45               v   51           v   52           v   53           v   54           v   55                        
 
 If v ij  presents one element of the matrix [vij] then 
 
v 11 = 84 I·G□1□·f□t 1 □□
 
v 21 = 85 I·G□1□·f□t 2 □□
 
v 31 = 86 I·G□1□·f□t 3 □□
 
v 41 = 87 I·G□1□·f□t 4 □□
 
v 51 = 88 I·G□1□·f□t 5 □□
 
v 12 = 85 I·G□2□·f□t 1 □□
 
v 22 = 86 I·G□2□·f□t 2 □□
 
v 32 = 87 I·G□2□·f□t 3 □□
 
v 42 = 88 I·G□2□·f□t 4 □□
 
v 52 = 84 I·G□2□·f□t 5 □□
 
v 13 = 86 I·G□3□·f□t 1 □□
 
v 23 = 87 I·G□3□·f□t 2 □□
 
v 33 = 88 I·G□3□·f□t 3 □□
 
v 43 = 84 I·G□3□·f□t 4 □□
 
v 53 = 85 I·G□3□·f□t 5 □□
 
v 14 = 87 I·G□4□·f□t 1 □□
 
v 24 = 88 I·G□4□·f□t 2 □□
 
v 34 = 84 I·G□4□·f□t 3 □□
 
v 44 = 85 I·G□4□·f□t 4 □□
 
v 54 = 86 I·G□4□·f□t 5 □□
 
v 15 = 88 I·G□5□·f□t 1 □□
 
v 25 = 84 I·G□5□·f□t 2 □□
 
v 35 = 85 I·G□5□·f□t 3 □□
 
v 45 = 86 I·G□5□·f□t 4 □□
 
v 55 = 87 I·G□5□·f□t 5 □□
 
 in which 
 
 f□t 1 □□f□t 2 □□f□t 3 □□f□t 4 □and f□t 5 □ are the fluctuating factors of the total ion beam during different integrating time t 1 □t 2 □t 3 □t 4 □t 5 , and G(j) denote the gains of the amplifiers A 1 , A 2  . . . , A 5 , respectively. According to some regular, selecting elements v ij  and eliminating the same factors, an equation can be established: 
 
□v 11 ·v 33□ /□v 13 ·v 31□ □□ 84 I· 88 I □ /□ 86 I· 86 I □ □□ 84 Sr/ 86 Sr □m ·□ 88 Sr/ 86 Sr □m    (1) 
 
 where the index m denotes measured value. 
 
      By the mass fractionation correcting equation in the first reference paper ( G. J. Wasserburg et al., Precise determination of Sm/Nd ratio, Sm and Nd abundances in standard solutions, page 2315), if  
                 •   ⁢             88     ⁢   Sr     /     Sr     •   ⁢           ⁢   n                 86       ⁢           ⁢   •   ⁢           ⁢   •   ⁢           ⁢                     88     ⁢   Sr       /     Sr     •   ⁢           ⁢   m                 86       ·   •     ⁢           ⁢   1     +     α   ⁢           ⁢     •     (     88   -   86     )           =       •   ⁢               88     ⁢   Sr     /     Sr     •   ⁢           ⁢   m                 86       ·   •     ⁢           ⁢   1     +     α   ⁢           ⁢     •   2                 (   2   )             
 
 then 
 
□ 84 Sr/ 86 Sr □n □□ 84 Sr/ 86 Sr □m ·□1+α□ (84-86) □□ 84 Sr/ 86 Sr □m ·□1+α□ −2    (3) 
 
 whereαis isotope fractionation factor per atomic mass unit and the index n denotes normalized ratio. 
 
 Substituting (2) and (3) into (1), we get 
 
[□ 84 Sr/ 86 Sr □n ·□ 88 Sr/ 86 Sr □n ] 1 □□v 11 ·v 33□ /□v 13 ·v 31□   (4) 
 
 where □ 84 Sr/ 86 Sr □n  and □ 88 Sr/ 86 Sr □n  are just the normalized dilution isotope ratios we want to get. 
 
 Using similar procedure we can establish more similar equations from the spectrum matrix [v ij ]: 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 1 □□v 14 ·v 23□ /□v 13 ·v 24□   (5) 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 2 □□v 23 ·v 32□ /□v 22 ·v 33□   (6) 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 3 □□v 32 ·v 41□ /□v 31 ·v 42□   (7) 
 
[□ 87 Sr/ 86 Sr □n ·□ 87 Sr/ 88 Sr □n ] 4 □□v 41 ·v 55□ /□v 45 ·v 51□   (8) 
 
[□ 84 Sr/ 86 Sr □n ·□ 88 Sr/ 86 Sr □n ] 2 □□v 34 ·v 51□ /□v 31 ·v 54□   (9) 
 
 where all the ratios of strontium are just the normalized dilution isotope ratios which we want to get. 
 
 From the equations□4□, (5), (6), (7), (8) and □9□□we can draw a interesting conclusion: 
 
 Using the invented technology, we can establish some equations every one of which contains products of pairs of normalized ratio of Sr. The product can be calculated through selecting elements v ij  of a spectrum matrix [v ij ] according to some regulation. The equations are independent of gains of the amplifiers and also independent of isotope fractionation factor α. Solving the equations the normalized ratios of Sr can be obtained directly. 
 
 For undiluted analysis, □ 88 Sr/ 86 Sr □n  □8.37521, the equations can be easily solved. 
 
 For dilution analysis, the equations can neither be solved lonely nor be solved by combining each other. Firstly, □ 84 Sr/ 86 Sr 58 n and □ 88 Sr/ 86 Sr □n  can be solved using simultaneous equations of the combination of equation (4) or (5) with the following formulae which quoted from the second reference paper (Boelrijk, N. A. I. M., “A general formula for “double isotope dilution analysis”, Chemical Geology, 3(1968), 323-325): 
 
[S 1 −□ 84 Sr/ 86 Sr □n ]/[□ 84 Sr/ 86 Sr □n −N 1 ]□[S 2 −□ 88 Sr/ 86 Sr □n ]/[□ 88 Sr/ 86 Sr □n −N 2 ]  (10) 
 
 where S 1 , and S 2  represent isotope ratios  84 Sr/ 86 Sr□ and  88 Sr/ 86 Sr of the spike; N 1  and N 2  are constants and represent naturally occurring isotope ratios  84 Sr/ 86 Sr and  88 Sr/ 86 Sr respectively. 
 
 Two pairs of solutions of the ratios  84 Sr/ 86 Sr□ and  88 Sr/ 86 Sr can be solved and the others may be solved easily. 
 
 Supposing one of the solutions of ratio□ 88 Sr/ 86 Sr □n  is 
 
[□ 88 Sr/ 86 Sr □n ] 2 □K   (11) 
 
 substitute equation (11) into equation (5), (6), (7) and (8) respectively the solutions of ratio□ 87 Sr/ 86 Sr □n  will be 
 
[□ 87 Sr/ 86 Sr □n ] 1 □√{square root over ((V 14 ·V 23 )·K/(V 13 ·V 24 ))}  (12) 
 
[□ 87 Sr/ 86 Sr □n ] 2 □√{square root over ((V 23 ·V 32 )·K/(V 22 ·V 33 ))}  (13) 
 
[□ 87 Sr/ 86 Sr □n ] 3 □√{square root over ((V 32 ·V 41 )·K/(V 31 ·V 42 ))}  (14) 
 
[□ 87 Sr/ 86 Sr □n ] 4 □√{square root over ((V 41 ·V 55 )·K/(V 51 ·V 45 ))}  (15) 
 
 Therefore, four values of ratios □ 87 Sr/ 86 Sr □n  and two values of ratios □ 84 Sr/ 86 Sr □n  are obtained in one cycle of scan. This character cannot only improve the efficacy of analysis but can also monitor the measuring system. Normally the values of the same ratio should be exactly the same respectively within the fluctuation of the measuring system. 
 
      The contribution of spike to naturally occurring isotope ratio ( 87 Sr/ 86 Sr) can be corrected by the following formula which is similar with the equation (3.12) quoted from reference 3 (Derek york: The Earth&#39;s Age and Geochronology) or the equation (2) quoted from reference 4 (Qiao G-sh, Normalization of isotope dilution analysis—A new program for isotope mass spectrometric analysis, Sciences in China (Series A), No. 10 (1988), page 1264) 
 
N i □□ 87 Sr/ 86 Sr □n +[□ 87 Sr/ 86 Sr □n −S i ]·□N 1 −□ 84 Sr/ 86 Sr □n □/□□ 84 Sr/ 86 Sr □n −S 1 □□  (16) 
 
 where Ni is the isotope ratio  87 Sr/ 86 Sr and has been normalized and corrected the contribution of spike, i.e., Ni is just the naturally occurring isotope ratio  87 Sr/ 86 Sr of the sample. 
 
      If the quantity of spike is zero then □ 84 Sr/ 86 Sr □n−&gt;N1 , the second term in the correct formula will be zero and the formula still be valid. This kind of zero spike dilution analysis will be called “virtual dilution analysis” which had been suggested by the inventor in reference 4.  
      The concept of “virtual diluted isotope analysis” is a useful suggestion. It makes that both the dilution analysis and the undiluted analysis can be done by the same mass spectrometric method and the same program, therefore the analysis procedure is simplified and the quality of the measure result is improved.  
     EXAMPLE 2  
      Basically the example 2 is similar to example 1. The difference is as follows: the integrating times ti is three ( i=1, 2, 3) instead of five (i=1, 2, . . . , 5) as example 1 where the scan is a full rotated peak jumping cycle; sometimes all the output signals of the A 1 , A 2 , A 3 , A 4  and A 5  are read but sometimes only part of them are read as shown in  FIG. 1 ,  FIG. 6  and  FIG. 7 .  
      For diluted isotope analysis, the first work is chemical analysis which includes isotope dilution procedure. The isotope ratios of the spike are known as  84 Sr/ 86 Sr═S 1 □ 88 Sr/ 86 Sr═S 2  and  87 Sr/ 86 Sr═Si. In the sample two of the naturally occurring isotope ratios  84 Sr/ 86 Sr═N 1  and  88 Sr/ 86 Sr═N 2  where N 1  and N 2  are constants 0.056584 and 8.37521 respectively.  
      The second is isotope dilution analysis using thermal ionization mass spectrometer. After the ion beam appeared in the monitor of the mass spectrometer, adjust the magnet field and the collectors so that the ion beams of  84 Sr,  85 Rb  86 Sr,  87 Sr and  88 Sr of the sample are collected stably and statically by the collectors Fj (j=1, 2, . . . , 5) through peak centering technique. Suppose that the currents of the amplified ion beams are  84 I,  85 I ,86 I,  87 I and  88 I respectively. Then:  
      1, In the first integrating time t 1  as shown in  FIG. 1 , which is the first “peak jumping” schematic diagram of thermal mass spectrometer equipped with a virtual amplifier, the amplifiers Aj(j=1, 2, . . . , 5) read the signals of isotopes  84 Sr,  85 Rb  86 Sr,  87 Sr and  88 Sr respectively controlled by the relay matrix R 1 .  
      2, In the second integrating time t 2  as shown in  FIG. 6 , which is the second “peak jumping” schematic diagram of thermal mass spectrometer equipped with a virtual amplifier, the amplifiers Aj(j=1, 2, . . . , 4) read the isotopes  85 Rb  86 Sr,  87 Sr and  88 Sr respectively controlled by the relay matrix R 1 . It should be noted that the amplifier A 5  is not used and should be empty.  
      3, In the final integrating time t 3  as shown in  FIG. 7 , which is the third “peak jumping” schematic diagram of thermal mass spectrometer equipped with a virtual amplifier, the amplifiers Aj (j=1, 2, 3) read the isotopes  86 Sr,  87 Sr and  88 Sr respectively controlled by the relay matrix R 1 . It should be noted that the amplifiers A 4  and A 5  are not used and should be empty.  
      The integrated signals can be filled in the following table which is a spectrum table of one cycle of scan.  
                              Spectrum Table of       One Quintuple Collector 3 Virtual Peak Jumping Scan                                                 V1   V2   V3   V4   V5                       t1   84   85   86   87   88           t2   85   86   87   88   empty           t3   86   87   88   empty   empty                         V1, V,3 . . . V5 are the outputs of amplifiers A1, A2, . . . A5 respectively                t1, t2, t3 are integrated times of the peak jumps                The numbers in the table represent the intensities of integrated signals corresponding to the mass numbers.             
 
      The spectrum table can be expressed as a matrix [vij]:  
                    V   11           V   12           V   13           V   14           V   15               V   21           V   22           V   23           V   24           V   25               V   31           V   32           V   33           V   34           V   35                        
 
      If v ij  presents one element of the matrix [vij] then 
 
v 11 = 84 I·G□1□·f□t 1 □□
 
v 12 = 85 I·G□2□·f□t 1 □□
 
v 13 = 86 I·G□3□·f□t 1 □□
 
v 14 = 87 I·G□4□·f□t 1 □□
 
v 15 = 88 I·G□5□·f□t 1 □□
 
v 21 = 85 I·G□1□·f□t 2 □□
 
v 22 = 86 I·G□2□·f□t 2 □□
 
v 23 = 87 I·G□3□·f□t 2 □□
 
v 24 = 88 I·G□4□·f□t 2 □□
 
 v 25  is empty 
 
v 31 = 86 I·G□1□·f□t 3 □□
 
v 32 = 87 I·G□2□·f□t 3 □□
 
v 33 = 88 I·G□3□·f□t 3 □□
 
 v 34  is empty 
 
 v 3  is empty 
 
      As in example 1, selecting elements v ij  according to some regular and eliminating the same factors, equations similar to equation (1) can be established. Using the same way as in example 1, all the ratios of strontium will be solved.  
      Summarily, in the examples for practicing the method of the invention, there should be no less than five collectors which collect mass number  84 ,  85 ,  86 ,  87  and  88  respectively; and a completed cycle of scan includes no less than three times integrating which measure the signals of the mass number respectively.  
      Conclusion: through all of the description above, the invention has some advantages clearly as follows:  
      1, the gain calibration is done during measurement instead of being done before the measurement start, i.e there isn&#39;t any extra rotation of virtual peak jumping for gain calibration between every two blocks during the measurement.  
      2, it can normalize the isotope ratios of dilution analysis of strontium automatically, so that isotopic fractionation can be corrected and the calculated concentration of strontium will be more reliable.  
      3, the naturally occurring isotope ratio of strontium can be calculated from dilution analysis of strontium with the same accuracy and precise as that of undiluted analysis. Therefore the work of both chemical analysis and mass spectrometric analysis are cut down about fifty percent.  
      4, the invented method can correct the contamination of spike to the chemical blank or the memory of the spike inside mass spectrometer automatically.  
      5, in the mass spectrometric analysis, the ion beams are collected by the corresponding collectors using static scan model which overcomes the disadvantage of dynamical scan model and makes the procedure of measurement simplified and easy to operating.  
      6, the method can not only measure dilution analysis of strontium but it can also measure undiluted analysis, i.e., virtual dilution analysis, without any change and the precise and accuracy is better than that of the convenient method.  
      7, in the method, the isotope ratio and the concentration of strontium are determined from the same share of a sample; therefore the unevenness of the geology sample can be avoided.  
      There will be some change, revisers and/or complementary easily happened to the description based on the embodiment content. But it can be understand that all of the changes, revisers and complement are involved in the spirit and the field of the invention described above.