J H Batey
Workshop on measurement characteristics and use of quadrupole mass spectrometers for vacuum applications
Bled, Slovenia, April 10–13, 2012

Paul & Steinwedel 1956 DE 944900

Examples of quadrupole construction

Typical quadrupole RGAs from c. 1982
Anavac SX200

Modern RGAs

Typical analytical quadrupole from c. 1990

A novel geometry: circular axis to make a compact instrument

1
Liverpool microquadrupole mass filter
Rods 0.5 mm diameter r0 0.22 mm
Length 20 mm
2

Mass filters come in a wide range of sizes …
1: ICP-MS
L: 230mm r0: 5.5mm
2: RGA (SX200)
L: 125mm r0: 2.7mm
3: RGA (Anavac)
L: 50mm r0: 2.7 mm
4: Microquad
L: 20mm r0: 0.22 mm
1 2 3 4

Isotope separators: quadrupoles on an altogether different scale!
Finlan, Sunderland & Todd,
Nucl. Inst & Methods,
195 (1982), 447-456
Von Zahn,
Zeitschrift fur Physik,
168 (1962), 129-142 r
0
: 13.5mm
L : 3 metres r
0
: 35mm
L : 5.86 metres

Early mass spectrometer: Dempster 1918
Recognizable components:
• Vacuum system
• Source
• Mass analyzer
• Detector
Isotope studies on alkali metals

Main components of a mass spectrometer
Main components can be identified in
Dempster’s system

Quadrupole mass spectrometer

Ion source
Electron-impact source is the commonest. The design can be quite complex for analytical mass spectrometers.
Filament; source electrode; extraction optics
Source voltage; electron energy
Repeller; collimating magnets

RGA source
For an RGA the source is of relatively simple construction – it resembles an extractor ion gauge.

Source
General requirements :
• Physical size
- usually “small enough”
• Sensitive
- typically 10 -4
• Robust
• Linear
A/mbar
- beware of log/log plots
• Reproducible
• Serviceable
- easy to dismantle/reassemble
• Low power; low voltage
• Non-invasive;
- that is, operating the mass spectrometer should not alter the vacuum composition
Desirable features
• Keep electrons confined to source
- avoid electron background signal
• Variable electron energy
- helps separate some species
• Low outgassing
- minimise materials
• Avoid trapped volumes
memory effects
• Closed or open?
- depends on application
• Choice of filament material
- tungsten, thoria, yttria

Linearity: beware of “log-log” plots!
Which would you rather have?

Source
General requirements :
• Physical size
- usually “small enough”
• Sensitive
- typically 10 -4
• Robust
• Linear
A/mbar
- beware of log/log plots
• Reproducible
• Serviceable
- easy to dismantle/reassemble
• Low power; low voltage
• Non-invasive;
- that is, operating the mass spectrometer should not alter the vacuum composition
Desirable features
• Keep electrons confined to source
- avoid electron background signal
• Variable electron energy
- helps separate some species
• Low outgassing
- minimise materials
• Avoid trapped volumes
memory effects
• Closed or open?
- depends on application
• Choice of filament material
- tungsten, thoria, yttria

Electron energy
Reduce electron energy to
40eV: eliminates interferences due to Ar2+
Better detection limit for water in argon

Source
General requirements :
• Physical size
- usually “small enough”
• Sensitive
- typically 10 -4
• Robust
• Linear
A/mbar
- beware of log/log plots
• Reproducible
• Serviceable
- easy to dismantle/reassemble
• Low power; low voltage
• Non-invasive;
- that is, operating the mass spectrometer should not alter the vacuum composition
Desirable features
• Keep electrons confined to source
- avoid electron background signal
• Variable electron energy
- helps separate some species
• Low outgassing
- minimise materials
• Avoid trapped volumes
memory effects
• Closed or open?
- depends on application
• Choice of filament material
- tungsten, thoria, yttria

Filaments
Tungsten
• Simple
• Mechanically robust
• Affected by oxidising/reducing gas
• Runs hot, so outgassing problems
• Rapid burn-out if vacuum leak
• OK with halogens
Thoria-coated iridium
• Coating is delicate
• More stable in oxidizing/reducing gas
• Cooler, so less outgassing
• Resistant to burn-out
• Not good for halogens
• Weak a emitter – possible health issues?
Yttria-coated iridium
• Generally similar to thoria, with no radiation worries.

Detector
Faraday plate/collector
Simple and robust.
Electron background and/or secondary electron emission may be a problem
(easily prevented).
Electron multiplier
Higher sensitivity; needs high voltage supply; more prone to calibration drift; not suitable for coarse vacuum
Discrete dynode multiplier; SCEM; micro-channel plate

QUADRUPOLE
Hyperbolic electrodes to give 2D hyperbolic field. Though in practice round rods are often used.
F
(x,y,z) =
F
0
. (x 2 – y 2 )
2r
0
2
Here
F
0 is 20V

QUADRUPOLE
“Saddle” shaped 3D field plot.
X field is proportional to the X co-ordinate
Y field is proportional to the Y co-ordinate.

QUADRUPOLE
The quadrupole structure can be used as a static device (that is, one in which the applied voltage
F
0 is constant) for steering and shaping an ion beam, with no mass selection. But for a mass filter, the potential
F an alternating component. Specifically
0 consists of a constant and
F
0
= U – V cos (2 p f (t-t
0
) ) where
U is the constant (“DC”) potential
V is the alternating (“RF”) potential f is the frequency of the RF supply t is the time t
0 is the initial phase of the RF component

QUADRUPOLE
Influenced by this field, the ions travel on complex trajectories in the X and Y directions, with a constant drift along the Z axis.

QUADRUPOLE
Mathieu equation

QUADRUPOLE
The significance of the stability region becomes clearer when it is plotted in terms of
V and U for a particular case r
0
= 6 mm f = 2x10 6 Hz
(typical values for a quadrupole ICP-MS)

QUADRUPOLE
Conceptual mass spectra, deduced from the stability diagram.

QUADRUPOLE
These peak shapes have been calculated using numerical integration of the Mathieu equation.
Field radius (r0): 6 mm
Radio frequency: 2 MHz
Field length:
Input radius:
200 mm
1 mm
Exit radius:
Ion energy:
6 mm
5 eV
Beam divergence 5 degrees
Ion masses 1, 2, 3, 4 & 5 amu

QUADRUPOLE
A basic quadrupole model is provided with the Simion package.
The dynamic voltages are programmed using the Lua language.

SIMION QUADRUPOLE
Round rods give a field that is essentially hyperbolic near the axis, but well away from the axis, the field is quite different.
10V
+10V +10V
10V
10V
+10V
10V
+10V
-10V
Potential contours at intervals of 2V
+10V +10V
-10V
-10V
+10V +10V
-10V
Gradient contours, at intervals of 1V/mm

Quadrupole field in X and Y directions
DC constant +20V. No RF applied.
r
0
= 2.76 mm
RF 0V, DC 20V: potential well in X direction
20
-3 -2 -1
0
0
-5
-10
-15
-20
15
10
5
V(x) dV(x)/dx r0
1 2 3
RF 0V, DC 20V: potential hill in Y direction
20
-3 -2
15
10
-1
5
0
0
-5
-10
-15
-20
V(y) dV(y)/dy r0
1 2 3

Ion motion in RF & DC quadrupole field
X component of ion motion.
Vary RF amplitude.
DC + 20V
RF = 0 r
0
= 2.76 mm
F = 2 MHz
M = 40 amu
RF = 0
DC - 20V
RF = 103
DC - 20V
RF = 145
DC - 20V
RF = 78
RF = 60
RF = 79
RF = 70
RF = 104 RF = 105
RF = 146 RF = 147

SIMION QUADRUPOLE
Plot the values of RF and
DC that give stable and unstable X trajectories.

SIMION QUADRUPOLE
Now add stability for Y trajectories (mirror image about DC = 0 axis).
The ion motion is stable for RF and DC values within the region bounded by the four coloured lines.

SIMION QUADRUPOLE
A Simion model, using parameters as listed by Taylor & Gibson. Hyperbolic rods (but note
T&G used round rods).
S Taylor & JR Gibson,J Mass Spectrom 2008; 43: 609–616
S Taylor & JR Gibson,J Mass Spectrom 2008; 43: 609–616

SIMION QUADRUPOLE
4%
2%
0%
39.7
12%
10%
8%
6%
39.8
39.9
amu
Peak
40.0
40.1
Mathieu stability region and scan line
Hyperbolic electrodes. The 50% peak with is 0.117 amu, corresponding to a resolution of
343. The peak is shifted to lower mass by 0.015 amu; presumably a smaller grid size would give a smaller shift.

SIMION QUADRUPOLE
Now we change to round rods …
S Taylor & JR Gibson,J Mass Spectrom 2008; 43: 609–616

SIMION QUADRUPOLE
Mathieu stability region and scan line Peak

SIMION QUADRUPOLE: 3D
2D
3D model with fringing field: transmission is increased and the lowmass tail is reduced
3D

SIMION QUADRUPOLE: 3D
The previous slide showed an unusually narrow peak. Usually a quadrupole is tuned to give a wider peak. This is data from the same Simion model, but with the scan line set to give a peak width 1 amu at 50% height. The peak is much smoother, and there is no lowmass tailing. This would be an excellent performance for an analytical quadrupole, such as an ICP-MS, for which abundance sensitivity of 1 ppm or better is needed. The flat peak top is rarely seen in practice, though examples have been reported.

Flat-topped peaks!
Some very early quadrupole papers showed flat-topped peaks. Is there still room for improvement from 21 st century manufacturers?
W Paul, HP Reinhard & U von Zahn,
Zeitschrift fur Physik,152 (1958), 143-182
Brubaker,
Recent developments in Mass Spectrometry,
Proc. Int. Conf. on Mass Spectrosc., Kyoto,
Japan, 1969, Pub Univ. of Pank, Baltimore, 1970
R = 1.16 R0 (for round comparison)
L = 25.4 cm; r0 = 6.55 mm
Hyperbolic, 1.414 MHz, 1 eV, aperture 1.27 mm

SUMMARY
• Quadrupole: versatile – wide range of design possibilities
• The mechanical design of current RGAs mostly follows longestablished design principles …
• … but there is increasing interest in smaller devices
• Simulation (e.g. with Simion) allows theoretical performance to be investigated in considerable detail.
AREAS NOT COVERED (in this talk).
• Electronics
• Data systems
• Calibration