A high-resolution focussing “dipole” mass spectrometer

53 International Journal of Mass Spectrometry @ Elsevier Scientific Publishing Company,

A HIGH-RESOLUTION

12 (1973) 53-6.5 - Pzinted in The Netherlands

and Zon Physics,

Amsterdam

FOCUSSING

“DIPOLI?’

MASS

SPECTROMETER

P. I-l. DAWSON Centre

de Recherches

QuPbec

I@

(Received

SW Ies homes

et les MoiPcuIes,

FacuItP

des Sciences,

UniuersitP &ma!,

(Canada)

2 December

1972)

ABSTRACl

A high-resolution focussing “dipole” mass spectrometer is proposed and its properties are explored by the computer calculation of ion trajectories. The device has a field corresponding to half that of a quadrupole mass mter and consists of two hyperbolic rods and 2 plane grounded electrode. Low energy ions are injected transversely to the instrument axis. It is shown that by -using the focussing properties of quadrupoIe fields, both a high resolution 2nd a large mass range should be possible while preserving the usual advantages of quadrupole mass spectrometers.

INTRODUCTION

Since the pioneering work of Patti et al-r the use of quadrupole fields in maSs spectromet,ry has been extensively studied’ 2nd in particular the quadrupole mass filter has found wide application. The mass filter, as implied by the name, transmits only ions of a small range of m_/evalues. Other ions have unstable trajectories so that their amplixdes of transverse oscillation become large 2nd the ions are lost from the device. There is a hhering rather than a focussing action. The principal advantages ‘of the mass filter have been the absence of a magnetic field, the compactness, rapid electronic scanning and, in some cases, the relative independence of instrument performance on initial ion energy. The Iimitations have been (a) the difZculties of achieving resolving powers gre2ter than 1000 without a great loss of sensitivity due to the rapid increase in oscillation amplitudes as the stability boundary is approached and (b) the high r-f. voltages required at

high masses. The amplitude cf the required high frequency voltage between

54 opposite

pairs of rods is proportional

to the m~~/e ratio2, as follows

v = 412 - mjf? - r&3

0)

where r. is half the rod separation, w is the angular frequency of the applied field and 4 N 0.706 at high resolution. The requirements of a high V at high masses could be eased by use of a lower frequency. However, the mass filter resolving power depends, in part, on the number cycles an ion spends in the field, n. For an ion of a given mass and a given injection energy, the maximum resolving power attainable is proportional to 02. Therefore the problem of very high voltages for high masses can only be overcome by sacriking resolution or building longer instrluments. The mass filter merely uses the path stability properties of quadrupole fields as expressed in the Mathieu equation of motion; ions of a m/e higher than those transmitted are unstable in the x direction and ions of a lower m/e are unstable in the y direction. However, the exact focussing properties of quadrupole fields under certain well-defined (a, q) conditions are well known. _4n attempt was made to utilize these properties with the invention of the monopole b;r von Zahn3. The monopole diagram (Fig.

no longer depends on stability properties near the tip of the stability 1) but uses a lower ratio a/q as a scan line. The mass separation

line for

0.2

0.3

0.4

0.5

0.6

0.7

0.8

o-9

1.0

Fig. 1. The a, q stability diagram for ion motion in a quadrupole field. The /Ix and /?, lines indicate tbe type of ion motion in the x and y directions, the fundamental frequency of ion oscillation being given by wo = p42 where (L)is the angular frequency of the applied field.

depends on the nature of ion trajectories near the y stability boundary.Von Zahn considered the possibility of utilizing focussing in both x and y directions simultaneouslybut subsequent computer simulations have shown that the monopole,

55 used with ion injection parallel to the instrument axis, only involves a partial focussing in the y direction and none in the x directionS 5. Recent work6 as commonly

has demonstrated

the importance of fringing fields in achieving high perfkynce

with this mode of operation. Lever7 in 1964 showed that a two-directional-focusing monopole (that is, using hoth x and y directions), should be possible with ion injection at a small angle to the instrument axis. He suggested that application of this principie should make possible the achievement of very high resolution in a small device. The exact focussing in two directions occurs only for certain specific pairs of (a, q) vaiues some of which Lever tabulated. Ions are focussed after an exact number of r-f. cycles within the field. This means that since ions are travelling along the axis of the instrument, they must all have precisely the same veIocity in order to be focussed on the exit hole and to produce a high resolution_ Hence, one of the attractive features of the mass fifter was to be sacrificed in return for the promise of high resolution in a short device. However, the circular entrance aperture would have to be small to retain the high resolution, the small area thus limiting instrument sensitivity_ In magnetic sector instruments, for example, the very narrow rectangular entrance and exit slits necessary for high resolution still have appreciable aperture area. There are no literature descriptions of the operation of a monopole in the mode suggested by Lever but a resolution better than 3G0 in a 30 cm long device has recently been attained’. In this paper, a two rod and plate structure (which might be called a “dipole” example) is proposed in order to exploit the exact following the “monopole” focussing properties of quadrupole fields. The novel feature is the injection of the ions transversely (Fig. 2) to the rUd direction_ The objectives are (a) to obtain very high resolution in a compact instrument, (b) to retain the quadrupole mass filter’s relative independence from initial ion energy (rendering a velocity selector

Ion exit

(0)

I

t

Ion

entrance

+

W

Fig_ 2. (a) A sketch of the proposed device showing the two hyperbolic rods and the ground electrode with symmetrically placed entrance and exit slits; (b) A cross-sectional view.

56 unnecessary), (c) to be able to operate the device at lower r-f. frequencies without loss of resolution so that voltage requirements are not exorbitant at high masses, and (d) to utilize rectangular entrance and exit slit systems so that] aperture, area remains appreciable even with narrow ‘slits. The possible operating points in the a, q stability diagram are some of those proposed by Lever and there is some similarity with this proposed monopole. However, the changes in geometry produce some fundamental differences in performance. The method of operation of the instrument is described below and its properties are explored by means of the computer calculation of ion trajectories.

INSTFX.JMENT DESIGN

Figure 2a shows a sketch of the proposed instrument and Fig. 2b a crosssection. It consists of two hyperbolic rods and a ground plane. Ion entrance and exit slits are placed symmetrically in the ground plane. Between the two rods a constant voitage U and an alternating voltage Y cos ot are applied. The field is exactly the same as that in half a quadrupoie structure. The conventional x, y directions are indicated on the figure. The ions are injected transversely to the rods from a position x O = y, wrth initial velocities Q. and - &,. The z. velocity will generally be close to zero. The ions leave the instrument at the position -x0, with velocities (when focussed) of -- _Coand Zo. That is, the field is required to produce an inverted “image” in both x and y directions. If r. is the minimum distance from the centre of the field to the rods, the equations of motion in the x and y directions are expressed by the Mathieu equation’ -y.

d*u + [a- 2q cos 2(< - <,)]u = 0 de* where 5 = of/2 and &, represents the initial phase of the alternating voltage when the ion enters the field qY = -qx

= 2eV/mr02i02

ay = -a,

= 4eU/mro2w2.

The properties of the Mathieu equation are described by the stability diagram as shown in Fig. 1. This is made up of superimposed stability diagrams for the x and y directions *. For (a, q) values inside the triangular area, the ion trajectories are stable (of limited amplitude) in both x and y directions. The nature of ion motion is defined by the /A, values. The fundamental frequency of the ion oscillation in a particular coordinate direction is given by w. = @3/2 and other superiiposed frequencies by

57 o1

=

(1 -

5)

0,

o-, =

(1 +

90

etc.

As pointed out by Lever7, an inverted image is formed after S field cycles when p = l/S and S is an integer. An inverted image will also be formed after S cycles when B = P/S and P is an odd integer (1 s P < S). Therefore ions will be transmitted by the instrument for (a, q) conditions where & = l/S and #& = P/S (1 5 P -C S and P is odd) subject to the condition that at all times y > x so that the ion does not prematurely strike the ground electrode. Table 1 lists some possible a, q operating points, taken from the work of Lever’. Values for P close to S can be excluded because the rapid oscillation in the x direction causes the ion to strike the grounded plane. TABLE VALUES

AS

I OF a (Upper)

CALCULATED

Values of S

AND

q (Iower)

SATISFYING

THE CONDITIONS

q)

=

l/S, px( --n, -_4)

=P/S

Values of P I

3

0.000 000

0.278436

0.126186 0.575 816

6

0.000000 0.233 150

0.095019 0.495 503

7

o.oooOao 0.200422

0.073 030 0.432 374

0.175636 0.633 358

8

0.000 000 0. I75 699

0.057492 0.382516

0.147256 0.576 545

9

0.000 000 0.156378

0.046272 0.342 500

0.123236 0.525286

10

0.000000 0.140869

0.037966 0.309 820

0.103 772 0.480 593

II

0.000000 0.128 150

0.03 1673 0.282 696

0.088 154 0.441966

12

0.000000 0.117532

0.026 802 0.259856

0.075 590 0.408 554

5

@,(ff,

SY LEVER’

The properties

of the proposed

5

instrument were examined by numerical

integration of the equations of motion using a computer so that ion trajectories could be examined4* 5z7 in detail for various conditions. Figure 3 illustrates the general nature of the trajectories involved and the influence of the choice of the P value. Figure 3a is a trajectory for &, = p, = l/la when the initial phase of the field CO equals 2.356 (the optimum for ion transmission). The equations of motion are linear with respect to u (that is, x and y) and therefore ion motion can be arbitrarily scaled. In this work, the initial displacements x0 and y. are always taken as unity. The initial velocities, in order to be

58

=v

Y

(7

(-I.-l)

(Cl

CO&

(1.I)

Fig. 3a.

I \

Fig. 3. Examples of ion trajectories for several possible choices of /?, and fix which give an inverted image after 10 cycles in the field. The initial y and x velocities were 0.05. (a) 8, = l/10, & = l/10(b) 8,. = l/IO, flz = 3/IO. The rod electrodes are shown by the dashed lines; (c) 8, = l/IO, /& = 5/10’

readily scaled, are best experessed in terms of [ 0. At other parts of the cycIe the field is unfavorable to ion entry into the device or the ions are quickly repulsed by the field and strike the grounded electrode (x .z=-JJ). Having demonstrated the principle of the device, we will now examine iti properties in more detail.

INSTRUMENT PEREORMANCE

This special case occurs. when a = 0; that is, when no constant voltage is applied _J&+WXIIthe rods. For a given applied voltage Y cos ot ions of Merent mass will be spread out aldng the “scan line”, a = 0, (Fig. 2) with -the lighter

60

(a)

w2!-1.02~ 1)

I (-.98,-238)

Fig. 4. An illustration of the variation of the focussing properties at the ion exit slit for the initial field phases&, = 0_6~,0.7x,0.8~ and O.% when q is varied: (al 8, = fix = l/IO; a = 0, (c)&=/3 E + I;lO; a=O,q=0.139869. q=O.140869; (b) &=flx i l/IO, a=O;q=0.141869;

masses farther.. from the origin. For any ion with & = #I, = l/S, where S is an integer, there will be exact focussing on the exit slit after a trajectory of the type shown in Fig. 3a. Figure 4a shows this focussing in detail for the case S = 10, q = 0.140869 for assumed initial velocities of * 10-l. The initial phases co = 0.627, 0.7x, 0.8~ and 0.97r are shown. The ions are focussed at the same point x = - 1, Y= - 1, for all these phases at exactly 10 cycles after the ions entered the field. This focussing is independent of the initiaI velocities, although the ions exit with velocities &, and -j,, . If slightly different q values are examined, the results are as illustrated in Figs. 4b and 4c. The ions are no longer focussed on the point - 1) and cross the plane x = y at different points, at different times and (-1, with differing velocities, even for this small change in q. The change in q corresponds, of course, to a change in the voltage amplitude V for an ion of a given mass m or to an ion of a slightly different mass at that same tied voltage amplitude V. It is evident that a spectrometer operating with the scan line a = 0 cannot be used for mass analysis in a simple way. As a “spectra” is scanned by varying q, an ion of a given mass will be transmitted each time /?, = /3, = l/S. At low q values (or high S) /? is very approximately proportional to q, so that the transmitted signal as q is varied would be a series of peaks spaced according to l/S for a given ion. Trajectory calculations similar to those of Fig. 4 but for /3= l/20 (q = 0.070644) show that there is a smaller displacement from the exit position for a given percentage variation in q when /3is smaller. In fact, about the same absolute variation in q is required to give the same displacement of the mean exit position. This suggests an overall transmission characteristic for a given ion would be as illustrated in Fig. 5, each transmission .peak being roughly of equal width.

61 S where

.I

&

= By = I/S

.2 (or

.3

Voltage

,

V

,

arbitrary

.4

units)

Fig. 5. -4 qualitative representation of the transmission characteristic for a single ion as the voltage Vis scanned when the AC. voltage U is zero. Ions are transmitted each time B = 1/S where S is an integer_

The diminished low voltages

at high

S suggests

due to the too large

intensity

amplitudes

qualitatively

the loss of sensitivity

at

of the ion oscillations.

This special case of 1R, - /?, = I/S might be useful in conjunction with very n&row slits to give high resolution but computer processing would be necessary to transform the complex spectra into a simple form in a similar way to the use of Fourier transform methods in optical spectroscopy. The muitiple peak transmission characteristic gives an advantage in sensitivity at the expenrs of computer processing the spectra.

This is a simpier, more directly useful case. For example, choosing operating conditions such that &, = l/1(3 and & = 3/10 corresponds to a scan line passing through the point a = 0.037951, 4 = 0.309700. (Note: there ars some very slight differences in the values found here for exact focussing by examination of ion trajectories and the values calculated by Lever as given in Table 1.) Only when the a, q value is at or near this vaIue is the ion transmitted. That is, the transmission characteristic is now a single peak as in a normal mass spectrometer. As previously stated, transmission can only occur during about 25 “/oof the r-f. cycle, when the field is favorable for ion entry. The resolving power for an instrument of a given size (given initial x and y displacements) can be estimated by examining ion trajectories at different points along the scan line. Figure 6(i) shows some exampies for &. = l/10, /I, = 3/10 for 5 initial phases of the ahernating field (eO = 2.042 to 2.670). At 4 = 0.309700, the focussing is not quite at the desired spot but all the phases are similar, the arrival time is about 10.04 periods after injection and the arrival velocities in the x and y directions are close to the initially assumed values of 0.05. The 0.1 % change in q, produced, for example, by a 0.1 0/ochange in the ion mass, gives a separation of about 1 0A in x

62 and y positions when the initial displacements are unity as illustrated by the groups of trajectories (b) and (d). The trajectories are no longer focussed. For (b), the arrival time at the plane x = y is roughly 10.12 periods and the arrival velocities are phase dependent, but of the order of 0.1. For (d)_the arrival time is about 9.92 periods after injection and the arrival velocities are roughly 0. !2. Clearly, the device gives an excelient mass resolution in relation to the initial displacements. However, the overall size of the device depends largely on the maximum y amplitude of the trajectories as can be seen in Figs. 3b and 3c. Table 2 compares the percentage separation of the mean exit position from unity for several diserent choices of /3,,and fi, for a 0.1 y0 variation in q jn each case. The maximum y deflection is TABLE SOME

2

EXAMPLES

INS-rRuhfEhT

OF

HOW

T-HE

CHOICE

OF

&

AND

/&

INFLUENCES

THE

RESOLVING

POWER

ANI,

THE

SIZE

The resolvingpowerdependson Qhe% variationin q. The assumed initial x and y velocities were -0.05

the x

and y exit values for a 0.1 % change in and f0.05 respectively. (See text.)

l/l0

3/10

0.0380

0.3097

1

4.2

l/10

s/10

0.1038

0.4806

5

7.2

l/l2

3J12

0.0268

0.2598

1.4

4.5

l/l2

S/12

0.0756

0.4085

5.9

7.0

also given. The assumed initial x and J velocities were t_ 0.05 in each case. The performance is seen to improve as the both S and P become larger. (However, note that for &, = l/12, p, = 7/12, the x oscillation is such that the ions strike the ground electrode (X > v) after only 1.9 periods.) Even higher performance could be achieved by choosing higher S values, apparently with oniy small increases in the device size. The higher S values would aIso be associated with somewhat lower voltages for a given mass. The focussing in this device does not depend on the initial x and y velocities, although transmission may be reduced if &, > fo. However, the maximum amplitudes will depend on the initial velocities as illustrated in Table 3 for the condition & = l/10, fix = 5/10. Initial x and y velocities up to about 0.1 are possible in these circumstances without a substantial increase in device size. To obtain the exact focussing, the q/a ratio must be precisely controlled to the desired value. It is interesting to examine the results of an error in the choice of scan line. Figure 6(G) shows the results of a 0.1% shift in the q/a ratio to 4.626 11 from 4.63124, the latter being the correct value for &, = l/10, & = 5/10. The

63 TABLE

3

DEPEM~~NCEOF~IAXI~~U~~~A~~PLITUDEONTHEINITIALXAND~VELOCITIE~

THE CASE/f$ = 1.110, /3= = 5!10.

(expressedintermsoft):

The initial displacements were unity in each case. Initial celocities (see text)

_&faxintunty amphhde

0

6.47 7.15 7.48 7.81 9.26

0.05 0.075 0.10 0.20

best focussing at the exit aperture is illustrated. The resolving power is obviously degraded. The mean arrival time of the ions is about 10.14 periods and the arrival velocities are about 0.2 compared with the initial velocities of 0.05.

position

of

A particular example

In judging the performance it is instructive to consider a particular example. Consider a device operating with & = l/10, /3, = 5/10; that is, with a = 0.103772, q = 0.480593. Let the initiai displacements be x0 = y. = 2.5 cm. The distance between entrance and exit slits is then 7.07 cm. Slit widths of 0.1 mm are commonly used in magnetic sector mass spectrometers whea electron multiplier detectors are employed. Assuming such slits would give suf&ient sensitivity in this case, one can use Table 2 to estimate a probable resolving power of about 15OdO. The trajectory calculations are not sufikiently accurate to check this estimate directly, but, in the case of larger mass variations, the dispersion is roughly proportional to Aq, (as illustrated in Fig. 6(i)). I n order to transmit aI1 initial velocities up to 0.1, a maximum y amplitude of 7.8 times the initial displacement must be allowable, which requires an r. of about 20 cm. The rods would have to be long enough to- avoid fringing field effects within this electrode gap. The actual values of the permitted velocities will depend on the chosen frequency as will the r-f. vokage required foi a particular mass. To avoid the requirement of high alternating voltages for high mass numbers, the frequency can be arbitrarily lowered, subject only to any limitation imposed by the maximlum for the initial ion energy. The voltage amplitude V = qo/2

m/e - ro2ix2

where q. is the operating point. However the maximum energy eE can be expressed as &VU&, hence V=

’

ro2

e

b

cl

I (-I.O2.-1.02)

(-1,-I)

b.98.

-.98)

I

1

(Tl.-l)

!-.98.--98)

Fig. 6. (i) An illustration of the ion trajectories near the exit slit for the scan line passing through & = 3/10, each set showing five initial phases of the alternating field (60 = 2.042 to 2.670). (a) close to the focusing position q = 0.309iO0, a = 0.037951; (b) p = 0.309391; (c) q = 0.309082; (d) q = 0.310009; (e) g = 0.310318. The initial X0 and F0 velocities were -0.05 and G-O.05 respectively. (ii) The best focussing at the exit slit obtainable when the q/a ratio is 4.626 11 instead of 4.63124 which would be the value for exact focussing with & = l/10, /3x = S/10.

the point 8,. = l/IO,

In the present case, q0 = 0.4806, I-, = 20 cm and V,,, = J(X=i +$z) = 1.44 x 0.1~~~x o/2 cm/set. Thus Y N 615OE. That is, to say, that for a maximum initial ion energy of 1 volt, an alternating voltage amplitude of 6000 volts would be sufficient to operate the mass spectrometer for any m/e ratio, provided that an appropriately low freqrlency is chosen for the higher masses. For a iixed frequency of operation, the maximum permitted initial ion velocity would be the same for all m/e. That is, the maximum permissable ion energy would be highest for the highest m/e. For an ion of 5000 mass units and a Y of 6000 volts, the frequency for the device of r, = 20 cm would be 17.5 kHz. A few further possibilities for improvement exist. For example, the ion signal is electively pulsed (20-25 y0 duty cycle) at the frequency of the applied field. Since the frequencies would generally be lower than in the normal mass kilter, the utilisation of a.c. detection techniques2s 6 (lock in amplification) should be straightforward.This might be particularly helpful, since only at the exact focussing position is the phase relation between entry and arrival times correctly preserved. For a source of we%defined ion energy, a further discrimination against nonexactly focussed ions is possible on the basis of the final ion energies. Non-focussed ions tend to have higher energies.

65 CONCLuSIONS

Computer calculation of ion trajectories in the proposed focussing two rod or “dipole” structure suggests the possibility of achieving high resolving power in a relatively compact device with a large mass range. These are two properties which

have been difficult to obtain with quadrupole

fields used conventionaliy.

The device

would operate with low energy ions ( s 1 eV) injected transversely to-the quadrupole field axis through a rectangular slit in the ground plane electrode. Entrance and exit through this plane would enable fringing field effects to be minimised. The length of the slits should ensure appreciable sensitivity even at high resolution.

The focusing

action

is relatively

independent

of initial ion energy and angle of

injection_ The instrument might thus make possible the extension of quadrupdle mass spectrometry with its inherent advantages to areas of application so far dominated by magnetic-sector instruments. The disadvantages of the proposed device are the necessity for exact shaping and positioning of the electrodes and of the exit and entrance slits (i.e. symmetrically) and the very high precision required in the control of the ~/LZratio. Another problem might be caused by distortion of ion trajectories by space charge but ion current densities would presumably always be small and, fiuthermore, ions entering the field at different initial field phases have somewhat different trajectories.

ACKNOWLEDGEMENTS

This work was funded by the Centre de Recherches sur les Atomes et les MolCcules which is supported by the National Research Council of Canada and

the Province

of Quebec.

REFERENCES 1

W.

PAUL, H. P. REINIURD AND U. VON ZAHN, 2. P~IT.,

152 (1958)

14%

A&an. Electron. Electron Phys., 27 (1969) 59. b, P. H. R. WHETTEN, in D. PRICE (editor), Dynamic Mass Spectrometry, Vol. 2,

2 a, P. H. DAWSON i\ND N. R. WHFI?EN, DAWSON

AND N.

Heyden and Sons, London, 1971. 3 U. VON i%HN, Reu. Sci. Instrum., 43 (1963) I. 4 P. H. DAWSON _+D N. R. WHETIEN, J. Vat. Sci. Technol., 6 (1969)

97.

5 P. H. DAMSON AND N. R. WHET-L-EN, Rev. Sci. 39 (1968) 1417. 6 H. DAW~~N. J. Var. Sci. Technol., 9 (1972) 487. 7 R. F. LEVER, IBM J- Res. Develop., 10 (1966) 26. 8 W. FOCK, Zst Australian Conference on Mass Specxrometry, 1972, personaZ communication.