Methodological Study on Measurement of Hydrogen Abundance in Hydrogen Isotopes System by Low Resolution Mass Spectrometry

Abstract

China's rapid economic growth has resulted in significant environmental side effects. Therefore, China has been interested in reducing her dependence on foreign oil and gas by developing technologies needed for hydrogen, in addition to her increasing energy mix of nuclear and renewable energy form, such as solar and wind power. There are three isotopes of hydrogen, i.e. protium (P or H), deuterium (D), and tritium (T). Both deuterium and tritium are important materials in nuclear fuel cycle industry. Tritium is one of the critical radioactive nuclides. Planning for and implementing contamination control as a part of normal operation and maintenance activities is an important function in any hydrogen facility, especially tritium facility. The development of hydrogen isotopes analysis is the key issues in this area. Mass spectrometry (MS) with medium (about 600) and high resolution (> 1,400) is commercially available; however, the routine analysis of hydrogen isotopes is done with low-resolution MS (< 200) in China. This paper summarizes the progress of MS measurement technology for hydrogen isotope abundance in China, focusing on our lab's research program and technical status. An analyzing method has been introduced for accurate measurement of tritium abundance in the H.D.T system by low resolution MAT-253 MS. The quotient of compression ratio coefficient is determined by building up equipment for laboratory-scale preparation of secondary standard gases and by considering the difference in sensitivity between hydrogen isotopes. The results show that the measured value is reproducible within the relative error range of 0.8% for gas samples of different tritium abundance.

1. Modified low-resolution MS analysis of hydrogen isotopes system with calibration coefficient

In theory, it is possible that an analysis of the six species (H2, D2, T2, HD, HT, and DT) of hydrogen isotopes system with low-resolution MS, since six individual mass peaks can be measured; i.e., six equations with six unknowns, as written below:

where I1, I2,…is the peak height of the various mass numbers measured, respectively, and a11,a12,…is the ratio of the following monatomic ions contribution to the peak height of the parent molecule, respectively, which can be measured or computed using the Frank-Condon principle10 (i.e. a11 is the ratio of the H+ on I1, a32 is the ratio of the D+ on I3, etc. ). The following reactions can be used:

(at room temperature).

The D2 component can be computed from the T2 and DT intensities, HT from the peaks at m/z 4, HD from Equation (3), and D2 from Equation (2). Results are summarized in the following equations:

where a11, a22, … are the coefficients of the various species on the various mass numbers. The coefficients for this analysis are the ratios of the monatomic contribution toward any one mass unit to the peak height of the parent molecule. The ratio of the monatomic contribution toward any one mass unit can be written as follows:

a11 = (0.323±0.001)%, a22 = (0.273±0.004)%, a33 = (0.220± 0.003)%, a12 = a21 = (0.297±0.004)%, a13 = a31 = (0.267±0.003) %, a23 = a32 = (0.245±0.004)%.

Abundance computation equations of hydrogen isotopes system can be written as follows:

where ϕ(H), ϕ(D), and ϕ(T) is the abundance of protium, deuterium, and tritium, respectively. Providing the mass discrimination is not too severe and high-purity calibration gases are available, mass discrimination can be managed using normal calibration procedures.

Improvements have been made by Shi Lei,12,13,16,17 Huang Gang,14 and Zhang Hai-lu15 using the compression ratio coefficient in low-resolution MS analysis of hydrogen isotope system. The following is the equations of abundance measurements in hydrogen isotopes system:

where k is the quotient of the compression ratio coefficients. k = 2.7203±0.0001) is determined based on building up equipment for laboratory-scale preparation of secondary standard gases and considering the sensitivity difference between hydrogen isotopes.

To make abundance measurements in hydrogen isotopes system more efficient, Shi Lei has modified the mass discrimination of ion optics. The following is the equation expressed by Shi Lei: 12,13,16,17

where F is the sensitivity quotient of various species of hydrogen isotopes system, as written below:

F(H2) = 1, FD2 = 0.975±0.001, FT2 = 0.904±0.002, FHD = 0.988±0.001, FHT = 0.9395±0.002, FDT = 0.952±0.002.

Five different samples were designed, and four comparisons were made by four separate organizations. The analyzing results between each other are comparable within the acceptable difference. The measuring results among the labs are comparative, indicating that the analytic method is reliable.

 

2. Problem of computing reaction equilibrium constants in hydrogen isotope abundance measurement with low-resolution MS

Mixtures of H2, D2, and T2 in the gass phase will not remain isotopically pure for a long time. The mixed molecules HT, DT, HD are rapidly formed in less than 24 h. Equilibrium is established in any concentration of all the molecular species according to the following process. The six hydrogen isotopes exchange the reactions published by Jones are shown in Table 2.10

Jones’ calculations gave the equilibrium constants at different temperatures from 25 K to 2500 K.10 It is important to note that all these constants are not independent, K1 = K3K4, K6 = K4K5, and K2 =K3K5.

However, it is impossible to have all the equilibrium constants at different temperatures. Shi Lei have established a theory of statistical mixing. All the equilibrium constant at different temperatures can be written as follows:12,13,16,17

Table 2.Equilibrium constants designations for isotope exchange reactions.

Table 3.Equilibrium constants for hydrogen isotopic equilibria.

By using equations 1-6 and considering the equation of D2 + T2 = 2DT, K2 is expressed as follows;

Equations 7-10 are rewritten as follows;

Hydrogen isotopes system abundance measurements in sampling temperature is of vital importance, especially from the view point of system control in the fuel processing system of the fusion reactor. Requirements are satisfied by the new formula for computation hydrogen isotope abundances in mass spectrometry.

 

3. Problem of computing ratios of monatomic ions in hydrogen isotope abundance measurement with low-resolution MS

Electron bombardment of the six diatomic molecular species resulted in the formation of the three monatomic ions, on a probability basis. When pure gases were bombarded, measurements of these ions resulted in the following typical values for the particular mass spectrometer:

The probability of forming the monatomic ions from the heteronuclear molecular species is difficult to measure and requires further computation. Although it is generally assured for such analyses that the “cross section” for forming diatomic ions from molecules by impact of 100 ev electrons is the same for all the isotopic species, a more careful approach must be taken for monatomic ion formation.

Table 4.The ratios of the following monatomic ions measured by experimentalists home and abroad.

Without analysis of the mechanics of forming these ions, there are two plausible procedures for predicting the forming of monatomic ions from the heteronuclear molecular species.10

a. An assumption that the difference in the ratios for the pure gases is characteristic only of the monatomic ion would indicate that aij = aii for all j, I1 = a11(2I11+I12+I13), etc. Such a procedure would predict for our instrument that a23 = 0.0027, which is in conflict with the value given above, but is approximately correct, and is a convenient handling of this second-order correction.

b. A more plausible assumption might be that an unsymmetrical molecule, XiXj, forms the Xi+ and Xj+ ions in equal amounts with aij = aji =(aij·ajj)0.5. It is rather tenable and probably accurate. This method was used throughout the present work.

The ratios of the following monatomic ions have been computed using the Frank-Condon principle with acceptable agreement with experimental values. In general, the absolute values of these ratios depend on the excess energy of the impact electrons above the threshold voltage for the process, and upon the physical temperature of the ion source, hence these ratios will vary between instruments. However, the ratio of the ratios can be expected to remain constant, and Schaeffer and Hastings10 gave values that are related as follows: a11 = 2.2a22 = 4.2a33. For simplification, R is defined as a22.

a11 = 2.2R; a33 = 0.53R; a12 = a21 = 0.74R; a13 = a31 = 0.50R; a23 = a32 = 0.38R

From the view point of Table 4, the ratio of the ratios of experiments vary from those using the Frank-Condon principle. It is realized that these assumptions are not totally justified.

Shi Lei12,13,16,17 revised the ratio of the ratios by volume of molecules of hydrogen isotopes using the theory of grand unification. New ratio of the ratios had been established. Following equations of the ratio of the ratios can be written as follows by Shi Lei:

a11 = 1.1R; a33 = 0.795R; a13 = a31 = 0.935R; a23 = a32 = 0.892R;

The ratio of the ratios revised by volume of molecules of hydrogen isotopes using the theory of grand unification is not in conflict with the experimental evidence.

 

4. Gas preparation of hydrogen isotopes standards

If suitable analyzers and accessory equipments are available, high resolution mass spectrometry should routinely analyze mixtures of the hydrogen isotopes system accurately within 0.5% under ordinary operating conditions, while low resolution MS should routinely analyze mixtures of the hydrogen isotopes accurately within 2% with accurately mixed standards.

Therfore, accurately mixed standards result in accurate MS analysis of hydrogen isotopes system. Shi Lei12,13,16,17 reviewed various methods of hydrogen isotopes gas preparation, including gravimetry, pressure, volume, infiltration, saturation, electro analysis and didution index methods. Zhang Hailu15 had established a gas preparation method, as illustrated by Figure 1. However, the gas preparation method worked with cryogenic active carbon flask that had the disadvantage of complex facilities, and the error of gas preparation was not been revised. Shi Lei12,13,16,17 has established a gas preparation method of deuterium and tritium, as illustrated by Figure 2. The results showed that preparation value was valid in the relative error range of 0.02% for the gas preparation method of deuterium and tritium. y = 1.03451x, r = 0.99235, where x is abundance calculated by the manometer, and y is the demarcated abundance.

Figure 1.cheme of experimental apparatus.

Figure 2.A gas preparation method of deuterium and tritium.

 

5. Conclusions

MS has been employed as a rapid measurement tool for hydrogen isotope abundance. Much attention has been paid to develop fully-automated MS analysis for hydrogen isotopes system. Although both medium and high resolution MS are commercial available worldwide for hydrogen isotopic abundance measurement, a low resolution MS method for the measurement of hydrogen isotopic abundance has been investigated. In China, a series of progress were designed and made, including methodological check, computations and modifications on measurement of abundance in hydrogen isotopes system, key techniques on gas preparation of hydrogen isotopes, contrast analysis of measurement of abundance in hydrogen isotopes system, and assessment of results of measurements and applying. Some interesting results were obtained. Thanks to the improvement, the measurement precision by the low resolution mass spectrometry goes down to less than 2%.