U.S. patent number 3,648,046 [Application Number 05/038,076] was granted by the patent office on 1972-03-07 for quadrupole gas analyzer comprising four flat plate electrodes.
This patent grant is currently assigned to Granville-Phillips Company. Invention is credited to Dean R. Denison, Charles F. Morrison, Jr..
United States Patent |
3,648,046 |
Denison , et al. |
March 7, 1972 |
QUADRUPOLE GAS ANALYZER COMPRISING FOUR FLAT PLATE ELECTRODES
Abstract
A quadrupole analyzer wherein the trajectory stability of the
charged particles is determined by two parameters a and q where
##SPC1## Where K = any value except 0.125 .ltoreq.K .ltoreq. 0.126.
A further aspect of the invention relates to performance
optimization of a quadrupole analyzer in the presence of relatively
large amplitude, nonquadrupole field components.
Inventors: |
Denison; Dean R. (Boulder,
CO), Morrison, Jr.; Charles F. (Boulder, CO) |
Assignee: |
Granville-Phillips Company
(Boulder, CO)
|
Family
ID: |
21897966 |
Appl.
No.: |
05/038,076 |
Filed: |
May 18, 1970 |
Current U.S.
Class: |
250/281;
250/292 |
Current CPC
Class: |
H01J
49/4215 (20130101) |
Current International
Class: |
H01J
49/42 (20060101); H01J 49/34 (20060101); B01d
059/44 () |
Field of
Search: |
;250/41.9DS |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Stolwein; Walter
Assistant Examiner: Church; C. E.
Claims
What is claimed is:
1. A quadrupole mass analyzing device for analyzing charged
particles by charge to mass ratio comprising four flat plate
electrodes disposed within the device where a first nonadjacent
pair of said electrodes is separated by a first distance and a
second nonadjacent pair of said electrodes is separated by a second
distance, and means for applying superimposed DC and sine wave AC
voltages to said electrodes, the voltages applied to said first
pair of electrodes being equal and the voltages applied to said
second pair of electrodes being equal and being opposite in
polarity to the voltages applied to the first pair of
electrodes.
2. A quadrupole device as in claim 1 where said first distance
equals said second distance.
3. A quadrupole device as in claim 2 where said first pair of
electrodes are parallel to one another and said second pair of
electrodes are parallel to one another.
4. A quadrupole device as in claim 1 where said first pair of
electrodes are parallel to one another.
5. A quadrupole device as in claim 4 where said second pair of
electrodes are parallel to one another.
6. A quadrupole device as in claim 4 where said second pair of
electrodes are coplanar.
7. A quadrupole device as in claim 6 where each of said second pair
of electrodes is (1) narrower in width than each of said first pair
of electrodes and (2) disposed between said first pair of
electrodes.
8. A quadrupole mass analyzing device for analyzing charged
particles by charge to mass ratio comprising four flat plate
electrodes symmetrically disposed within the device where a first
nonadjacent pair of said electrodes has applied thereto a first
voltage (U+V cos wt) and a second nonadjacent pair of said
electrodes has applied a second voltage -(U+V cos wt) thereto
where
U=a DC voltage;
V=the half-amplitude of an AC voltage;
w=the angular frequency of the AC voltage; and
t=time.
9. A quadrupole device as in claim 8 where each said flat plate is
disposed in proximity to the two plates adjacent to it so that the
array of said plates is square in cross section.
10. A quadrupole device as in claim 8 where said plates are
disposed parallel with respect to one another.
11. A quadrupole device as in claim 8 where each of said flat
plates comprises a thin, metallic ribbon disposed on a support.
12. A quadrupole device as in claim 8 where said device includes at
least one source of potential in addition to the DC and AC voltages
applied to said four electrodes, the dimensions of each electrode
being such that the coefficient C.sub.1 in the expression
.phi.(r,.theta.)=C.sub.o (r/r.sub.o).sup.2 cos2.theta.+C.sub.1
(r/r.sub.o).sup.6 cos 6.theta.+--C.sub.n
(r/r.sub.o).sup.2(2n.sub.+1) cos2(2n+1).theta.
where .phi.(r,.theta.)=the potential due to the applied fields at
radius r and angle .theta. with respect to the axis of symmetry of
said electrodes, r.sub.o =the distance from the axis of symmetry to
said electrodes, and C.sub.1, C.sub.2 --C.sub.n are constants
defined by the potentials applied and the dimensions of the
structure, is no more than 10 percent of the value of C.sub.o.
13. A quadrupole device as in claim 12 where the potential is the
potential on a cylindrical tube which surrounds said four
electrodes and where each said flat plate is disposed in proximity
to the two plates adjacent to it so that the array of said plates
is square in cross section.
14. A quadrupole device as in claim 13 where said cylindrical tube
is grounded.
15. A quadrupole device as in claim 14 where said plates are
symmetrically disposed within said tube, the radius of said tube
being R and where the width, 2l, of each plate is approximately
specified as follows:
where r.sub.o =the distance from the center of said array of plates
to the surface to said plates.
Description
BACKGROUND OF THE INVENTION
This invention relates to an improved quadrupole-type gas analyzer
for separating charged particles, usually positive or negative
ions, by utilizing electric fields to separate said charged
particles by their charge to mass ratio.
In 1953, Paul and Steinwedel introduced the concept of using a time
varying quadrupole field as a mass separator and in 1955, Paul and
Raether demonstrated that a practical device could be produced to
separate ions of differing mass.
The theory of Paul and Steinwedel assumes that the electrode
structure required to generate the quadrupole field consists of
hyperbolic cylinders or electrodes 10-16 (see FIG. 1) with semiaxes
both equal to a distance r.sub.o, the so-called field radius. The
hyperbolic cylinders 10-16 are connected to alternating and direct
current sources such that the two electrodes 10 and 12 on the X
axis receive a voltage (U+V cos w t) where U is the DC voltage, V
is the half-amplitude of the AC voltage, w is the angular frequency
of the AC voltage, and t is time and the two electrodes on the y
axis receive a voltage -(U+V cos w t). Thus, the DC polarity of the
y axis electrodes is reversed from the X axis electrodes and the
two sets of electrodes have AC voltages 180.degree. out of phase
from each other.
Although an admitted oversimplification, the mass separation can be
visualized in the following way. With some set of AC and DC
voltages on the electrodes, ions with masses that are lighter than
some value will be strongly influenced by the AC voltage and will
remain in phase with that voltage. Thus, energy will be taken from
the field and the amplitude of the motion of such a particle will
increase until it is captured on an electrode. An ion with mass
heavier than some value will not be affected appreciably by the AC
field and will be dragged to one of the y axis electrodes by the DC
field. It then follows that there is some mass such that the AC and
DC fields tend to balance each other and such a mass will follow a
stable trajectory through the analyzer. More theoretically, the
equation of motion of an ion through the combined AC-DC field can
be expressed as a linear sum of Mathieu functions where the ion
trajectory stability is determined by two parameters, a and q,
defined by
where m is the ionic mass and e is the charge. a and q are related
in a complex way. Graphically, a and q can be plotted as in FIG. 2
and the stability criteria intuitively described above can be
determined. The shaded region contains those values of a and q
(this is actually only one of many stability regions--but the most
useful in a practical device) for which an ion executes a stable
trajectory through the analyzer. For a constant ratio of DC and AC
voltages, the ratio of a to q is a constant and is graphically
represented by the straight line, commonly referred to as the
"working line," as shown at 20 in FIG. 3. For an analyzer with a
given value of r.sub.o and operating at some frequency w, it can be
seen from the definitions of a and q that the ionic masses can be
considered to be spread out along the working line with the heavier
masses nearer the origin. As the voltages are scanned from zero to
some maximum value, with the ratio of a to q, and hence DC to AC
voltage ratio, held constant, the masses slide along the working
line with only those masses falling within the stability region
executing stable trajectories. Thus, as the voltage is scanned from
zero to some value a plot of the ion current passing through the
analyzer as a function of the voltage a mass spectrum is generated.
The working line as shown in FIG. 3 intersects the stability region
such that some range of masses execute stable trajectories, as
indicated at 22. As the slope, and hence the ratio of a to q, is
increased the range becomes narrower until intersection of the
working line with the stability diagram occurs at only one point
and hence only a single mass executes a stable trajectory. Thus, as
the slope of the working line is increased, the resolution
increases. Obviously if the slope of the working line is increased
further, no ions execute stable trajectories. This, then, is
briefly how the analyzer functions.
In actual practice, the difficulty and expense of producing
precision hyperbolic electrodes has forced the expedient of
approximating the hyperbolic surfaces with cylindrical surfaces. In
the literature, the teaching has been that the most satisfactory
substitution is a round rod with a radius of 1.15 r.sub.o in
analogy to a field study of a magnetic quadrupole made by I. E.
Dayton. Further, the teaching of the literature claims that such
substitution of round rods of radius 1.15 r.sub.o for the
hyperbolic surfaces is an expedient only, and that degradation of
performance results.
However, it has been determined by the inventors that the above
teaching is not true and that unexpectedly improved results are
obtained by deviating from that teaching.
DETAILED DESCRIPTION OF THE DRAWING
FIG. 1 is a cross-sectional illustration of a prior art quadrupole
analyzer.
FIG. 2 is a graph illustrating one of the stability regions of the
analyzer of FIG. 1.
FIG. 3 is a graph illustrating the operation of the analyzer of
FIG. 1.
FIG. 4 is a graph which illustrates stability regions or diagrams
obtained for a number of round rod diameters.
FIG. 5 is a graph which illustrates the diagrams of FIGS. 4, 8, and
10 when normalized.
FIG. 6 is a graph illustrating K as a function of round rod radius
for round rod analyzers.
FIG. 7 is a cross-sectional illustration of a flat plate analyzer
in accordance with this invention.
FIG. 8 is a graph which illustrates a stability region or diagram
associated with the analyzer of FIG. 7.
FIG. 9 is a cross-sectional illustration of a circular concave
analyzer.
FIG. 10 is a graph which illustrates a stability region or diagram
associated with the analyzer of FIG. 9.
FIG. 11 is a cross-sectional illustration of a modified quadrupole
in accordance with the invention.
FIG. 12 is a diagrammatic illustration of one embodiment of the
flat plate analyzer of FIG. 7.
FIG. 13 is a diagrammatic illustration of one embodiment of the
circular concave analyzer of FIG. 9.
FIG. 14 is a diagrammatic illustration of one embodiment of a small
wire analyzer in accordance with the invention.
FIG. 15 is a diagrammatic illustration of a circular concave
analyzer together with an enclosure therefor in accordance with a
further aspect of the invention.
FIG. 16 is a diagrammatic illustration of a flat plate analyzer
together with an enclosure therefor in accordance with a further
aspect of the invention.
DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS OF THE INVENTION
Theoretical analysis of the potential distributions of various
electrode arrangements have been made and stability diagrams
similar to FIG. 2 have been established. Each of the arrangements
which were analyzed will now be discussed. Generalized conclusions
will then be stated.
Round Rod Analyzer
An analytic expression for the potential in the vicinity of round
rods, with potentials as described for FIG. 1, is not readily
obtained. However, the potential distribution was obtained
numerically by constructing a grid and computing a solution to
Laplace equation using the Liebmann process. Once the potential
distribution is known, the x and y potential gradients are
obtainable and thus the forces on an ion at any point within the
rod structure are known. A computer is then employed to "follow" an
ion through the rod structure and determine those values for the AC
and DC components of the voltage impressed on the rods for which a
stable trajectory is obtained. FIG. 4 shows the stability diagrams
obtained for a number of rod diameters. The parameters .alpha. and
.delta. used in the figure are analogous to the a and q of the
hyperbolic analyzer of FIG. 1. They are defined as
The important thing to note in FIG. 4 is that these stability
diagrams have the same shape but differ in size from the a-q
diagrams of FIG. 2. FIG. 5 shows that if each diagram is normalized
to a peak value of .alpha.=.delta.=1, all the diagrams fall on top
of each other including the diagram for the hyperbolic analyzer.
Thus it can be concluded that
.alpha.=K.sub.1 a
and .delta.=K.sub.2 q
and from the definitions of .alpha., .delta., a, and q it can also
be seen that
2K.sub.1 =K.sub.2
so that
.alpha.=Ka
.delta.=2Kq
where K=0.125 for the hyperbolic analyzer, FIG. 6 shows K as a
function of rod radius for round rod analyzers.
It is thus apparent that a mass analyzer can be produced with rods
of radius differing from the formerly prescribed 1.15 r.sub.o where
K=0.126.
Flat Plate Analyzer
The flat plate analyzer corresponds to the case where the rod
radius becomes infinite and the analyzer takes the form shown in
FIG. 7 where the plates are indicated at 22-28. The solution to
Laplace's equation can be explicitly expressed for this
configuration. That is, ##SPC2##
where x" and y" are the x and y components of the acceleration on
the particle as a function of position and time. These are not
readily integrable to give x and y as functions of time, however,
they were numerically integrated using a computer to give values of
.alpha. and .delta., as defined before, for which an ion would have
a stable trajectory. When this is done, the diagram of FIG. 8
results. Again, this normalizes onto the same diagram shown in FIG.
5 which again implies that
.alpha.=Ka
and .delta.=2Kq
The value for K for the square analyzer is 0.116.
Circular Concave Analyzer
If the plates of FIG. 7 are bent into segments of a circle, the
electrode structure of FIG. 9 where the plates are shown at 30-36,
is obtained. The potential for this case also can be written
explicitly and is found to be
The differential equations of motion can again be numerically
integrated to give the stability diagram of FIG. 10. This figure
also normalizes onto the diagram of FIG. 5 and so again
.alpha.=Ka
and .delta.=2Kq
The value of K for the concave analyzer is found to be 0.109. The
authors (1) T. Hayashi and N. Sakudo and (2) M. Y. Bernard
discussed the possibility of using circular concave electrodes.
These authors, however, have approached the problem from the point
of view that the hyperbolic analyzer represents the ideal and the
attempt is made to select an angle subtended by the circular
electrodes such that spatial components of the field higher than
the quadrupole component are eliminated or, at least, minimized.
The analysis presented in this disclosure point to the conclusion
that such minimization is neither necessary nor even desirable. If
all higher spatial field components were eliminated, leaving only
the quadrupole component, the value of K would increase to 0.125,
i.e., the value of K for the hyperbolic analyzer, and the
advantages of the lower K value would be forfeited.
Conclusions
The invention derives from conclusions to be drawn from the
foregoing analyses.
The first conclusion is that any symmetric array of four electrodes
can be used for mass separation. Secondly, each array of electrodes
has a particular value of K relating the .alpha. and .delta.
parameters to the hyperbolic a and q parameters. Further
implications of the second conclusion are as follows. If the
following values are substituted into the expressions for the
hyperbolic a and q parameters--that is e=1.6.times.10.sup.- .sup.19
coulombs, one atomic mass unit =1.67.times.10.sup.- .sup.27
kilograms, and the angular frequency =2.pi..times.10.sup. 6 f where
f is expressed in megahertz, the following expressions are
obtained. ##SPC3##
where M is the mass of the ion in atomic mass units and r.sub.o is
expressed in centimeters. The choice of resolution fixes the ratio
of a and q and thus we may use the quantity V/Mf.sup.2 r.sub.o.sup.
2 as a "figure of merit" for various types of electrode
configuration. The lower the value of this quantity, the lower is
the voltage necessary to apply to the analyzer electrodes to allow
a given mass to pass through the analyzer for some given frequency
and field radius. The generation of high voltages at high frequency
is not a desirable condition. The operating point for high
resolution for a hyperbolic analyzer is at q=0.7068, thus
This parameter for several differing structures is given in the
following table.
Structure V/Mf.sup.2 r.sub. o.sup.2
__________________________________________________________________________
hyperbolic array 7.218 1.15 r.sub.o radius round rod 7.317 0.01
r.sub.o radius round rod 31.8 0.001 r.sub.o radius round rod 51.1
flat plate array 6.750 circular concave array 6.320 10 r.sub.o
radius round rod 6.918
__________________________________________________________________________
Thus a more efficient mass analyzer is obtained in the sense that
the flat plate or concave array can operate at potentials lower
than the hyperbolic array given the same mass, frequency of the AC
voltage, and field radius. It must be reiterated here that the
results obtained for the square and concave analyzers are novel and
unexpected. The computer analysis shows that specific mass
separation can be achieved at lower values of K (and hence lower
values of V/Mf.sup.2 r.sub.o.sup. 2) than for a pure quadrupole
field, i.e., the field produced by hyperbolic electrodes. Specific
mass is defined to be the mass to charge ratio for an ion. The
advantages are manifold: simpler electronics, higher transmission
coefficient for the analyzer, lower cost construction, to name just
a few. Precision ground rods are very expensive but low cost, thin,
metallic ribbons (see ribbons 40-46 of FIG. 12) can be stretched to
give a very precise flat surface for a flat plate array or
precision bore quartz tubing (see 50 of FIG. 13) can be obtained at
very modest cost with the inside metallized (see 52-56 showing
three of the electrodes in FIG. 13) to produce a concave array. The
small wire (see wires 60-66 of FIG. 14) analyzers (0.01 r.sub.o and
0.001 r.sub.o rod sizes, for example) do not have the advantage of
low voltages but they allow very open light construction with the
"rods" consisting of taut wires. For a small mass range application
such as upper atmosphere research, such a structure has the
advantage of very low weight. It is clear from the analysis
presented in this disclosure that many other electrode forms may be
used to advantage in differing applications. Thus, the teaching
that the hyperbolic electrode analyzer is the optimum electrode
structure and that a round rod structure with rod radius equal to
1.15 r.sub.o is the best approximation to the hyperbolic structure
is not true for all applications. Structures with K values
differing from these two have many superior characteristics. The
analysis presented in this disclosure has been presented in terms
of electrostatic fields for the purpose of specific mass analysis
in a "quadrupole" type structure. However, the analyses are equally
valid for pole face contour in magnetic quadrupoles. These magnetic
quadrupole structures are used in the analysis by specific mass of
high energy particles as found in nuclear accelerators.
Referring to FIG. 11, there is shown a nonsymmetric quadrupole
structure having upper and lower plates 90 and 92 which extend over
the plates 94 and 96 to thereby provide a stable mechanical
structure. Although, as stated above the quadrupole is nonsymmetric
it is nevertheless illustrative of an instance of a structure
wherein the value of K is different from 0.125 but nevertheless
useful in some applications.
The quadrupole-type analyzers described hereinbefore are
satisfactory in resolution performance, but because of the presence
of relatively large amplitude, nonquadrupole field components, the
effective usable cross section of the analyzer is restricted for
some applications. For example, the usable radius of the concave
analyzer of FIG. 9 is 60 percent of r.sub.o where r.sub.o is the
radius of the electrodes. Thus the available cross section usable
as an analyzer in the concave device is only 36 percent of the
geometric cross section of the analyzer structure. The result of
this is to reduce the sensitivity of the device.
Referring to FIG. 15, there is shown an electrode structure
comprising electrodes 70-76 together with enclosing cylinder 78
which typically is grounded as indicated at 79. It can be shown
from the solution of Laplace's equation in cylindrical coordinates
that the potential within the electrodes 70-76 can be expressed in
the form
where r is the distance from the center of the electrode
structure.
The values obtained for the coefficients C.sub.0, C.sub.1, C.sub.2,
... are determined by the specific electrode structure chosen. For
the concave analyzer,
where .gamma. is one half the angle subtended by an electrode and
.phi.(.theta.) is the potential along the circular extension of the
electrode in the gap between adjacent electrodes as indicated at 77
in FIG. 15.
Referring to FIG. 16, there is shown a square analyzer comprising
electrodes 80-86 and enclosing cylinder 88 which typically is
grounded as indicated at 89. For the square analyzer, the
coefficients are somewhat more complex ##SPC4##
Here .phi.(r.sub.o, y) is the potential along the extension of any
one of the electrodes 80-86 to its corresponding corner of the
square as indicated for electrodes 84 and 82 at 85 and 87 for
example. l is the half width of the electrode.
The first term in the expansion of the potential for either of the
structures of FIGS. 15 and 16 is the quadrupole term. The second is
a 12-pole term, the third is a 20-pole term, etc. Since the C.sub.1
term is the second largest term in the expansion (C.sub.2 is
considerably less than C.sub.1), one can most closely approximate
the hyperbolic potential distribution by adjusting the electrode
size such that C.sub.1 =0. It has been determined that C.sub.1 is
approximately 10 percent of C.sub.0 for the square analyzer of FIG.
7. Thus, a deviation of 10 percent would be acceptable with the
square analyzer but preferably C.sub.1 should be made as small as
possible. Further, in fact, the value of C.sub.1 can be greater
than 10 percent of C.sub.0 in some configurations such as the
concave analyzer of FIG. 9 where C.sub.1 is 33 percent of
C.sub.0.
The potential in the gaps between the electrodes depends on the
potential distribution surrounding the electrode structure. A mass
analyzer is normally operated within a vacuum system of finite size
and therefore surfaces, either grounded or operating at some other
potential, occur in the vicinity of the electrode structure of the
mass analyzer. These surfaces influence the potential distribution
in the vicinity of the electrode structure and therefore influence
the values of the coefficients, C.sub.n. It therefore follows that
the size of each electrode, for which C.sub.1 =0, is influenced by
the presence of the external surfaces.
A computer was used to determine the potential in the gaps between
electrodes for the concave and square analyzers located inside a
grounded cylinder such as cylinders 78 and 88 of FIGS. 15 and 16
respectively. A grounded cylinder was chosen to illustrate the
effect of external surfaces because it represents the condition
most often encountered in actual practice. That is, a mass analyzer
operating in a vacuum system most often is surrounded by a vacuum
tight housing consisting of a metal tube which is electrically
grounded. This housing is open on one end so that it may be
attached to the remainder of the vacuum chamber in which the
materials to be analyzed are generated. It should be understood,
however, that this case is illustrative only and the technique used
here may be applied to any arrangement of surfaces with any chosen
potentials.
The Liebmann numerical process was used to solve Laplace's equation
for a series of grounded surface radii and the potential in the
gaps between electrodes was obtained. The integral in the
expression for C.sub.1 was then numerically evaluated and thus
C.sub.1 was obtained as a function of the electrode size. The
electrode size which gave C.sub.1 =0 was then obtained. If, as in
FIG. 15, R is the radius of the grounded surface, and r.sub.o is
the geometric radius of the analyzer, then the angle, 2.gamma.,
subtended by the electrode in the concave analyzer for C.sub.1 =0
is given by
Similarly, as in FIG. 2, the width of the electrode, 2l, in the
square analyzer for C.sub.1 =0 is given by
Here r.sub.o is the distance from the center of the electrode
structure to the electrode surface and the calculated length is
given as a fraction of r.sub.o to give a dimensionless
quantity.
If a representative example is taken and a stability diagram
obtained, then it is observed that the peak shifts toward the
.alpha. and .delta. values of the hyperbolic analyzer as C.sub.1
approaches zero.
The K value for the concave analyzer shifts from a value of 0.109
for 90.degree. electrodes to 0.118 for the case where C.sub.1 =0.
The K value for the square analyzer shifts from 0.116 for l=r.sub.o
to 0.123 for the case where C.sub.1 =0. The K value of a hyperbolic
analyzer is 0.125. Thus it is apparent that the optimization of the
electrode size has brought the field closer to that of a pure
quadrupole. For the square analyzer, the effective radius usable
for mass analysis increases from 0.6 r.sub.o to 0.85 r.sub.o as K
increases from 0.116 to 0.123. Since the available area, and thus
the sensitivity of the instrument, increases as the square of the
radius, the sensitivity increases by almost 100 percent as K
increases from 0.116 to 0.123. Similarly for the concave analyzer,
as K increases from 0.109 to 0.118, the effective radius increases
from 0.6 r.sub.o to 0.75 r.sub.o or an increase in sensitivity by
almost 60 percent.
Numerous modifications of the invention will become apparent to one
of ordinary skill in the art upon reading the foregoing disclosure.
During such a reading it will be evident that this invention
provides a unique quadrupole device for accomplishing the objects
and advantages herein stated.
* * * * *