RADIO-FREQUENCY MASS SPECTROMETER

Alongside the improvement of mass spectrometers whose operation is based on the deflection of a focused ion beam by magnetic and electric fields, in recent years new methods of mass spectrometry have begun to be developed through the selection of particles by velocity. Various versions of such selecting devices have been proposed and tested by a number of authors, and certain successes have been achieved\(^{1–7}\)*). Although the resolving power of mass spectrometers using velocity selection is, as a rule, not high (considerably lower than can be achieved in instruments in which particles are deflected by force fields), they nevertheless possess a number of advantages that make them especially valuable for analytical and industrial purposes. Their chief advantages are simplicity, portability, and low cost.

This class of selectors includes the original device developed by the author of the paper under review\(^{8}\). Being highly portable, it has a comparatively high mass resolving power (on the order of several percent) and can be successfully used as a mass spectrometer for gas-analysis purposes. In essence it is an ordinary multielectrode tube of specialized design, operating under properly selected conditions. This also determines one of its most important merits—high stability and the absence of any need for careful adjustment and maintenance. The special feature of the design is that, instead of cylindrical electrodes, plane electrodes are used, arranged parallel to one another. The principal technical requirement here is the high precision of the mutual arrangement and orientation of the electrodes, as well as the quality of their manufacture.

Fig. 1. Diagram of a single-stage selector.

*) See also the preceding abstract by K. Wulffson.

The scheme of a single-cascade selector is shown in Fig. 1. Electrons leaving the cathode \(K\) are accelerated by the potential difference between grid \(C_1\) and the cathode and, entering the space between grids \(C_1\) and \(C_2\), create in it (as a result of collisions with gas molecules) positive ions (the spectrometer operates well in the pressure range from \(10^{-4}\) to \(10^{-6}\) mm Hg). The ions formed in the space between grids \(C_1\) and \(C_2\) are accelerated by the field existing in this region and pass through grid \(C_2\), possessing an energy not exceeding the value \(qV\), where \(q\) is the ion charge and \(V\) is the potential difference between grids \(C_1\) and \(C_2\).

Let us now assume that grids \(C_2\), \(C_3\), and \(C_4\) are located at equal distances \(s\) from one another, that the potentials of grids \(C_2\) and \(C_4\) are equal, and that an alternating potential of cyclic frequency \(\omega\) is applied to grid \(C_3\). Then the field strength between grids \(C_2\) and \(C_3\) may be represented in the form:

\[ E_{23}=E\sin(\omega t+\theta), \]

and between grids \(C_3\) and \(C_4\):

\[ E_{34}=-E\sin(\omega t+\theta). \]

We shall count the time \(t\) from the moment when the given ion passes grid \(C_2\) and enters the space between grids \(C_2\) and \(C_3\), i.e. \(\theta\) denotes the phase of the alternating field at the moment when the given ion enters it. If the amplitude of the alternating potential on grid \(C_3\) is small in comparison with the potential difference \(V\) accelerating the ions, then the influence of the alternating field on the time of passage of the ion between grids \(C_2\) and \(C_4\) may be neglected, and to a first approximation this time may be taken equal to

\[ \frac{2s}{v}, \]

where the mean velocity of the ion \(v\) is determined by the well-known relation

\[ qV=\frac{1}{2}Am_0v^2 \]

(\(A\) is the mass number of the ion, \(m_0\) is the atomic mass unit).

Neglecting also the influence of space charge, it is not difficult to find the increment of the ion energy along the path between grids \(C_2\) and \(C_4\). It is equal to

\[ \Delta W=\frac{EqV}{\omega}\left[\cos\theta-r\cos\left(\frac{s\omega}{v}+\theta\right)+\cos\left(\frac{rs\omega}{v}+\theta\right)\right]. \]

The condition for the maximum of \(\Delta W\) leads to the expression

\[ \frac{s\omega}{v}+\theta=\pi, \]

where \(\theta=46^\circ 26'\), whence

\[ \frac{s\omega}{v}=133^\circ 34'. \]

Particles passing grid \(C_2\) at other values of \(\theta\) or with a velocity different from the optimal one will acquire a smaller additional energy.

The greatest value of the energy that an ion reaching grid \(C_4\) may have will be

\[ W_{\max}=qV+(\Delta W)_{\max}, \]

which for singly charged ions will occur when the condition

\[ A=\frac{0.266\cdot10^{12}V}{s^2\omega^2}, \]

is satisfied, where \(V\) is expressed in volts, \(s\) in cm, and \(\omega\) in hertz.

Thus, for a given frequency \(\omega\) and a given accelerating potential \(V\), only ions of a quite definite mass can have the optimum energy value.

If between grid \(C_4\) and the collecting electrode \(C.E.\) a retarding potential difference corresponding to an energy only slightly less than \(W_{\max}\) is applied, then only those particles whose mass number satisfies the optimum condition will be able to reach the collecting electrode, and the instrument may be used as a mass selector.

To estimate the resolving power of the device, let us turn to Fig. 2, \(a\), which shows the dependence of the additional energy \(\Delta W\), acquired by the ions on the path between grids \(C_2\) and \(C_4\), on the number \(N\) of periods of the change of potential on grid \(C_3\) during the motion of the ion in the alternating field (for the case when, at the moment when the ion passes through grid \(C_3\), the phase of the alternating field is equal to \(\pi\)). The position of the main maximum corresponds to the value

\[ N=\frac{2s\omega}{v}=267^\circ=0.74 \text{ period}. \]

If the retarding potential corresponds to an energy \(qV+Z\) (see Fig. 2), then particles for which

\[ \frac{2s\omega}{v} \]

lies in the interval from \(A\) to \(B\) will reach the collecting electrode (Fig. 2, \(a\)).

The corresponding dependence of the anode-current strength on the frequency of the alternating field for the case of positive mercury ions is shown in Fig. 3, \(a\). As is evident from the figure, the resolving power of such a device is very small. However, it can be considerably increased by the successive use of a number of selecting devices, i.e., by arranging in series in the tube several groups of three electrodes with the application to the middle electrode of each group of an alternating potential of the same frequency. In this case it is only necessary carefully to maintain both equality of the distances between the electrodes

Fig. 2. Dependence of the energy acquired by an ion in an alternating field on the number of periods covering the time of the ion’s stay in the alternating field: \(a\)—single-stage selector; \(b\)—two-stage selector; \(c\)—three-stage selector.

of each group, as well as the distances between individual groups. The external electrodes of each group must have identical potentials. Since the optimum condition is associated with a definite value of the phase of the alternating field at the moment when the ion passes the first electrode,

Fig. 3. Dependence of the anode current on the frequency of the alternating field for ions of a given mass: a—single-stage selector (mercury ions), b—two-stage selector (iodine ions), c—three-stage selector (mercury ions).

then the time required for an ion to traverse the distance from some electrode of one group to the corresponding electrode of the next group must be equal to an integer number of periods. Hence the distance between the exit electrode of a given group and the entrance electrode of the next group must be equal to

\[ (2.70\,n - 2)s, \]

where \(n\) is an arbitrary integer.

FROM CURRENT LITERATURE

In Figs. 2, б and 3, б are shown the corresponding dependences of \(\Delta W\) on \(N\) and of the anode current on \(\omega\) in the case of negative iodine ions at a pressure of \(10^{-4}\) mm Hg for a two-stage selector with \(n=6\).

In Figs. 2, в and 3, в are shown the corresponding curves (for positive mercury ions) in the case of a three-stage selector with \(n_1=9\) and \(n_2=7\). This choice of \(n_1\) and \(n_2\) was dictated by the requirement of the best elimination of secondary peaks. By increasing the retarding field, secondary maxima can be completely eliminated, as a result of which the picture shown in Fig. 4 is obtained. The vertical lines in this figure show the position and relative concentration of the various mercury isotopes.

Thus, a three-stage selector has a mass resolving power of about \(3\)—\(6\%\). It may be expected that a further increase in the number of stages will make it possible to raise it still more. The general appearance of a three-stage mass spectrometer is shown in Fig. 5.

Fig. 4. Mass spectrogram of mercury ions with a three-stage selector.

In practice it proves convenient to use an alternating potential of the same order as the accelerating one. This leads to certain changes in the operating potentials of the various grids, which we shall not discuss, just as we shall not discuss questions connected with the selection of negative charged ions, the need to be free of the masking influence of the electron current, and also the use, for the creation of ions, of an electron beam.

An extremely important characteristic of a mass spectrometer is its “luminosity.” As is clear from what has been said, the device described is free from slits or other devices that limit the cross section of the beam. The most significant factor determining the power of the ion beam is the transparency of the grids; thus, with a transparency of one grid of \(65\%\), the total transparency of the entire system of the three-stage tube would be only \(0.5\%\). At the same time, for good operation of the instrument it is necessary that the grids be “ideal,” i.e., that the sizes of the openings in the grids be small in comparison with the distances between the grids (in the described three-stage selector this condition was not fulfilled); since the distances between the grids are small (of the order

If \(2^\circ\) mm), then this condition imposes extremely stringent requirements on the technology of manufacturing the grids.

Fig. 5. General view of a three-cascade mass spectrometer.

The author made the grids from tungsten wire of diameter \(12.5\,\mu\) with apertures of about \(0.75\) mm.

Thus, the area of the apertures was about \(95\%\) of the total area of the grid, and the transparency of the three-cascade selector reached the enormous value of about \(50\%\) (the current in Fig. 3, \(в\), corresponds to approximately \(5\%\) of all ions formed in the apparatus).

In conclusion it should be noted that the mass spectrometer described does not require preliminary calibration with known ions and in this sense is an absolute instrument.

There is hardly any doubt that, after appropriate improvement, the mass spectrometer described will find wide application.

R. G.

CITED LITERATURE

1. W. R. Smythe and J. Mattauch, Phys. Rev. 40, 423 (1932).
2. S. H. Bauer, J. Phys. Chem. 39, 959 (1935).
3. W. F. Stephens, Phys. Rev. 69, 691 (1946).
4. P. B. Weisz, Phys. Rev. 70, 91 (1946).
5. A. E. Cameron and D. F. Eggers, Rev. Sci. Instr. 19, 605 (1948).
6. S. A. Goudsmit, Phys. Rev. 74, 622 (1948).
7. J. A. Hipple and H. A. Thomas, Phys. Rev. 75, 1616 (1949).
8. W. H. Bennett, J. Appl. Phys. 21, 143 (1950).