Mass Spectrometers

instruments used to separate the ionized particles of a substance (molecules and atoms) according to mass, based on the action of magnetic and electric fields on ion beams traveling in a vacuum. In mass spectrometers the ions are recorded electrically; in mass spectrographs they are recorded according to the darkening of the sensitive layer of a photographic plate placed in the instrument.

A mass spectrometer (Figure 1) usually contains a device for preparing the substance being studied (1); an ion source (2), where the substance is partially ionized and the ion beam is formed; a mass analyzer (3), in which the ions are separated according to mass, or, more accurately, usually according to the ratio of the mass m of an ion to its charge e; and an ion collector (4), where the ion flux is converted into an electric signal, which is then amplified and recorded. In addition to data on the number of ions (the ion current), data on the mass of the ions are also fed from the analyzer to the recording unit (6). A mass spectrometer also has electric power systems and devices that produce

Figure 1. Diagram of a mass spectrometer: (1) inlet system, (2) ion source, (3) mass analyzer, (4) ion collector, (5) amplifier, (6) recording device, (7) electronic computer, (8) power supply, (9) pumps. The evacuated part of the instrument is bounded by the broken line.

and maintain a high vacuum in the ion source and analyzer. Mass spectrometers are sometimes connected to electronic computers.

In any method of recording ions, the mass spectrum ultimately represents the dependence on m of the magnitude of the ion current I. For example, in the mass spectrum of lead (Figure 2), each peak of the ion current corresponds to singly charged ions of lead isotopes. The height of each peak is proportional to the content of the given isotope in lead. The ratio of the mass of an ion to the width δm of the peak (in units of mass), R = m/δm, is called the resolving power or resolution of the mass spectrometer. Since the width of the peak is different at different levels of relative intensity of the ion current, the quantity R is also different at different levels. For example, in the spectrum shown in Figure 2, R = 250 in the region of the peak of the isotope ²⁰⁸Pb at a level of 10 percent with respect to the amplitude of the peak, whereas R = 380 at a level of 50 percent (the half-amplitude). For a full characterization of the resolving power of an instrument, it is necessary to know the shape of the ion peak, which depends on many factors. The value of the greatest mass for which two peaks that differ in mass by one unit can be resolved to a given level is sometimes called the resolving power. Since for many types of mass spectrometers R is independent of the ratio m/e, these two definitions of R coincide. Mass spectrometers with R up to 10 are conventionally said to have low resolving power; with R ˜ 10²-10³, medium resolving power; with R ˜ 10,3-10⁴, high resolving power; and with R ω 10⁴-10⁵, very high resolving power.

Figure 2. Mass spectrum of thorium lead (δm_50% is the width of the peak at halfamplitude; πm_10% is the width of the peak at the level of one-tenth of maximum intensity)

There is no generally accepted definition of the sensitivity of a mass spectrometer. If the substance being studied is fed into the ion source in gaseous form, the ratio of the current generated by ions of a given mass of a specified substance to the partial pressure of the substance in the ion source is often called the sensitivity of the mass spectrometer. In instruments of different types, with different resolving powers, this quantity lies in the range of 10^-6 -10³ ampere per millimeter of mercury (A/mm Hg). The minimum content of a substance that can be detected using a mass spectrometer in a mixture of substances is called the relative sensitivity. For various instruments, mixtures, and substances it lies in the range of 10^-3-10⁷ percent. The minimum quantity of a substance in grams that must be fed into a mass spectrometer for the substance to be detected is sometimes taken as the absolute sensitivity.

Mass analyzers. The design principle of the mass analyzer is the basis for classification of mass spectrometers. A distinction is made between static and dynamic mass spectrometers. Electric and magnetic fields that are permanent or virtually unchanged during the passage of an ion through the instrument are used to separate ions in static mass analyzers. In this case ion separation is spatial: ions with different values of m/e move along different trajectories in the analyzer. In mass spectrographs, ion beams with different values of m/e are focused at different points on the photographic plate, forming bandlike tracks after development (the exit slit of the ion source is usually rectangular). In a dynamic mass spectrometer an ion beam with a given m/e is focused on the ion collector slit. The mass spectrum is formed (sweeps) upon a change in the magnetic or electric fields, as a result of which ion beams with different values of m/e enter the collector slit in succession. When a continuous record is made of the ion flux, a graph with ion peaks is obtained (Figure 2). Microphotometers are used to obtain in such a form the mass spectrum recorded on the photographic plate by the mass spectrograph.

A diagram of a standard static mass analyzer using a homogeneous magnetic field is shown in Figure 3 The ions formed at the ion source emerge from a slit of width S₁ in the form of a diverging beam, which is separated into ion beams with different m/e (m_a/e, m_b/e, and m_c/e) in the magnetic field, and the ion beam having a mass m_b is focused on slit s₂ of the ion collector.

Figure 3. Diagram of a static magnetic analyzer with a homogeneous magnetic field: (S₁) and (S₂) slits of the ion source and collector; (OAB) Region Of The Homogeneous Magnetic Field H₁ which is perpendicular to the plane of the figure. the thin solid lines indicate the boundaries of ion beams with different m/e, and r is the radius of the central trajectory of the ions.

The value of m_b/e is defined by the expression

where m_b, is the mass of the ion (in atomic mass units), e is the charge of the ion (in units of elementary electric charge), r is the radius of the central trajectory of the ions (in cm), H is the magnetic field intensity (in oersteds), and Fis the applied potential difference (in volts) by means of which the ions are accelerated in the ion source (the accelerating potential).

Analysis of the mass spectrum is made according to the change in H or V. The former is preferable, since in this case the conditions for “extraction” of ions from the ion source do not change over the course of the sweep. The resolving power of such a mass spectrometer is

where σ₁ is the beam width at the point where it enters the collector slit S₂.

If the focusing of the ions were ideal, then in the case of a mass analyzer for which X₁ = X₂ (Figure 3), σ₁ would be exactly equal to the width of the source slit S₁. In fact, σ ω S₁, which reduces the resolving power of mass spectrometers. The spread of the kinetic energy of the ions emerging from the ion source is one reason for the broadening of the beam. This is more or less inevitable for any ion source (see below). Other causes are the significant divergence of a given beam, the scattering of ions in the analyzer because of collisions with molecules of the residual gas, and the “repulsion” of the ions in the beam because of the likeness of their charges. “Inclined inlet” of the beam into the analyzer and curvilinear boundaries of the magnetic fields are used to reduce the influence of these factors. Nonuniform magnetic fields, as well as prism optics, are used in some mass spectrometers. To reduce ion scattering an attempt is made to produce a high vacuum in the analyzer (≦10^-8 mm Hg in instruments with average and high R). Double-focusing mass spectrometers, which focus on slit S₂ ions with identical m/e that emerge not only in different directions but also with different energies, are used to reduce the influence of the energy spread. For this purpose the ion beam is passed through not only a magnetic field but also through a deflecting electric field of special shape (Figure 4).

Figure 4. Example of a double-focusing mass analyzer. A beam of accelerated ions emerging from slit (S₁) of the ion source passes successively through the electric field of a cylindrical capacitor, which deflects the ions by 90°, and a magnetic field, which deflects the ions by another 60°, and is focused into slit (S₂) of the ion collector.

It is technically difficult to make S₁ and S₂less than a few microns. In addition, this would lead to very small ion fluxes. Therefore, it is necessary to use large R and correspondingly long ion trajectories (up to a few meters) in the instruments to obtain high or very high resolving power.

Different times for passage of the ions over a certain distance are usually used in dynamic mass analyzers to separate ions with different m/e. In addition to purely electrical analyzers, dynamic analyzers exist in which a combination of electric and magnetic fields are used. The action on ion beams of pulse or radio-frequency electric fields with a period less than or equal to the ion passage time through the analyzer is a common feature of dynamic mass analyzers. More than ten types of dynamic mass analyzers have been proposed, including time-of-flight (1), radio-frequency (2), quadrupole (3), farvitron (4), omegatron (5), magnetic-resonance, (6) and cyclotron-resonance (7). The first four types are purely electrical, whereas in the last three a combination of constant magnetic and radio-frequency electric fields is used.

In a time-of-flight mass spectrometer (Figure 5), ions are formed in the ion source by a very brief electric pulse and are “injected” in the form of an “ion packet” through the grid (1) into the analyzer (2), which is an equipotential space. As the initial packet “drifts” along the analyzer in the direction of the ion collector (3), it is “demixed” into a number of packets, each of which consists of ions with identical m/e. The demixing occurs because the energy of all ions in the initial packet is identical, and their velocities, and hence the passage time t through the analyzer, are inversely proportional to :

Here V is the accelerating potential and L is the length of the analyzer. The sequence of ion packets arriving at the collector forms the mass spectrum, which is recorded, for example, on an oscilloscope screen.

Figure 5. Diagram of a time-of-flight mass analyzer. A packet of ions with masses m₁ and m₂ (black and white circles) “thrown” into the analyzer through grid (1) moves in the drift space (2) in such a way that the heavy ions (m₁) fall behind the light ions (m₂); (3) ion collector.

In a radio-frequency mass spectrometer (Figure 6) the ions acquire an identical energy eV in the ion source and pass through a system of successive grid stages. Each stage consists of three equidistant plane-parallel grids (1), (2), and (3). A high-frequency electric field U_HF is applied to the central grid with respect to the two outside grids. When the field frequency aω and the ion energy eV are fixed, only ions with a specific m/e have a velocity v such that, as they move between grids (1) and (2) in the half-period when the field between them is accelerating for ions, they intersect grid (2) at the time of field sign change and pass between grids (2) and (3) also in an accelerating field. Thus, they receive a maximum energy increment and strike the collector. As ions of other masses pass through these stages, they are either slowed by the field—that is, lose energy—or receive an insufficient energy increment and are shunted away from the collector at the end of their path by the high stopping potential U₃. As a result, only ions with a specific m/e strike the collector. The mass of these ions is defined by the relation

where a is a numerical coefficient and S is the distance between grids. The analyzer is retuned to record ions of different masses by changing either the initial energy of the ions or the frequency of the HF field.

Figure 6. Diagram of a radio-frequency mass analyzer: (1), (2), and (3) grids that form a three-grid stage; high-frequency voltage U_HF is fed to central grid (2). On being accelerated within the stage by the high-frequency field, ions with a certain velocity—and hence a certain mass—receive a large increment of kinetic energy that is sufficient to overcome the braking field and to strike the collector.

In quadrupole mass spectrometers (Figure 7), ion separation is accomplished in a transverse electric field with hyperbolic potential distribution. The field is generated by a quadrupole capacitor (a quadrupole) that consists of four rods of round or square cross section that are symmetrical about and parallel to the central axis. Opposite rods are linked in pairs, and direct and alternating high-frequency potential differences are applied between the pairs. The ion beam is fed into the analyzer along the quadrupole axis through a slit (1). For fixed values of the frequency oω and the amplitude of the alternating voltage C/o, the amplitude of the oscillations in a direction transverse to the axis of the analyzer does not exceed the distance between rods only for ions with a certain value ofm/e. These ions pass through the analyzer by virtue of their initial velocity and, after emerging from it through the exit slit (2), are recorded upon striking the ion collector. Ions whose mass satisfies the condition

(where a is a constant for the instrument) pass through the quadrupole. The amplitude of oscillations of ions that have other masses increases as they move in the analyzer in such a way that they reach the rods and are neutralized. Retuning to record ions of other masses is accomplished by changing the amplitude U₀ or frequency ω of the variable component of the voltage.

Figure 7. Quadrupole mass analyzer: (1) and (2) inlet and exit slits of analyzer, (3) trajectory of ions, (4) high-frequency voltage generator

In a farvitron (Figure 8), ions are formed in the analyzer itself upon ionization of the molecules by electrons emerging from the cathode and oscillate along the axis of the instrument between the electrodes (1) and (2). When the frequency ω of the oscillations coincides with the frequency of the alternating voltage U_HF that is fed to the grid, the ions acquire additional energy, surmount the potential barrier, and reach the collector. The resonance condition has the form

where a is a constant for the instrument.

Figure 8. Farvitron: (1) and (2) electrodes between which ions oscillate

In dynamic mass spectrometers with a transverse magnetic field, ion separation according to mass is based on the coincidence of the cyclotron frequency of rotation of the ion in circular trajectories in a transverse magnetic field with the frequency of the alternating voltage applied to the analyzer electrodes. For example, in the omegatron (Figure 9) the ions move in arcs of a circle under the influence of the applied high-frequency electric field E and the constant magnetic field H. Ions whose cyclotron frequency coincides with the frequency oω of the field E move in a spiral and reach the collector. The mass of these ions satisfies the equation

where a is a constant for the instrument.

Figure 9. Analyzer of an omegatron

The constancy of the passage time for ions of given mass along a circular trajectory is used in magnetic-resonance mass spectrometers (Figure 10). Ions that are close in mass (the region of whose trajectories[I] is shaded), moving in homogeneous magnetic fields H away from the ion source(l), strike the modulator (3), where a fine packet of ions that begin to move in orbit (II) by virtue of the acceleration acquired in the modulator is formed. Further separation according to masses is accomplished by accelerating the “resonance” ions, whose cyclotron frequency is a multiple of the frequency of the modulator field. After several revolutions the ions are accelerated once again by the modulator and strike the ion collector (2).

Figure 10. Diagram of a magnetic-resonance mass analyzer; the magnetic field H is perpendicular to the plane of the figure

Resonance absorption of electromagnetic energy by ions takes place in cyclotron-resonance mass spectrometers (Figure 11) when the cyclotron frequency of the ions coincides with the frequency of the alternating electric field in the analyzer. The ions move along cycloids in homogeneous magnetic field H with a cyclotron frequency of orbital motion

(8) ω₀ = eH/mc

where c is the speed of light.

Figure 11. Cyclotron-resonance mass analyzer. A high-frequency electric field in the region of the analyzer makes it possible to identify ions with a given m/e from the resonance absorption of energy by the ions when the field frequency and the cyclotron frequency of the ions coincide.

For each type of dynamic mass analyzer the resolving power is determined by an intricate set of factors, some of which, such as the influence of the space charge and ion scattering in the analyzer, are common to all types of mass spectrometers, both dynamic and static. The ratio of the time in which the ions cover a distance equal to the width of the ion packet to the total flight time of the ion through the drift space plays an important role for instruments of group (1); for instruments of group (3) the number of oscillations of the ions in the analyzer and the relation between the constant and variable components of the electric fields performs such a function; and for instruments of group (5) the number of revolutions that an ion makes in the analyzer before striking the ion collector plays this role. High resolution has been achieved for some tvpes of dynamic mass spectrometers: for (1) and (3), R ~ 10³; for (6), R ~ 2.5 × 10⁴; and for (7), R ~ 2 × 10³.

For mass spectrometers with very high resolving power, and also for general-purpose laboratory instruments—in which high resolution, high sensitivity, a broad range of measurement of masses, and reproducibility of the results of measurements are required simultaneously—the best results are achieved with static mass spectrometers. On the other hand, in certain cases dynamic mass spectrometers are most convenient. For example, time-of-flight mass spectrometers are convenient for recording processes with a duration of 10^-2-10^-5 sec; radio-frequency mass spectrometers are promising in space research because of their small weight, dimensions and power consumption; by virtue of the small size of the analyzer, large range of measurable masses, and high frequency, quadrupole mass spectrometers are used in work involving molecular beams. Because of the high values of R at low intensities, magnetic-resonance mass spectrometers are used in the geochemistry of helium isotopes to measure very large isotopic abundance ratios.

Ion sources. Mass spectrometers also are classified according to the methods of ionization: (1) ionization by electron collision, (2) photoionization, (3) ionization in a strong electric field (field ion emission), (4) ionization by ion collision (ion-ion emission), (5) surface ionization; electric spark in a vacuum (vacuum spark), (6) ionization by laser beam.

These methods are most often used in analytical mass spectroscopy because of their relative technical simplicity and the large ion currents that are generated: method (1), in the analysis of volatile substances; method (6), in work involving poorly volatile substances, and method (5), in the isotopic analysis of substances that have low ionization potentials. Because of the large energy spread of the ions, method (6) usually requires double-focusing analyzers even to achieve a resolving power of several hundred. The values of the average ion currents created by an ion source that uses ionization by electron collision at an ion energy of 40-100 electron volts (eV) and for a source slit several dozen microns wide (which is typical of laboratory mass spectrometers) are 10^-10-10^-9 A. These currents are usually smaller for other methods of ionization. “Soft” ionization—that is, ionization of molecules that is accompanied by insignificant dissociation of the ions—is accomplished using electrons whose energy exceeds the ionization energy of the molecule by only 1-3 eV, and also by using methods (2), (3), and (4). The currents produced by “soft” ionization are usually of the order of 10^-12-10^-14 A.

Recording of ion currents. The values of the ion currents generated in mass spectrometers determine the requirements for their amplification and recording. The sensitivity of the amplifiers used in mass spectrometers is of the order of 10^-15-10^-16 A for a time constant of 0.1-10.0 sec. A further increase in the sensitivity or speed of mass spectrometers is achieved by using electron multipliers, which improve the sensitivity of current measurement in mass spectrometers to 10^-18-10^-19 A.

Approximately the same sensitivity values are achieved by using photographic recording of ions through long exposure. However, because of the low accuracy of measurement of ion currents and the clumsiness of the devices used to feed photographic plates into the vacuum chamber of the analyzer, photographic recording of mass spectra has retained some significance only for very precise measurements of masses, and also in cases when all lines of a mass spectrum must be recorded simultaneously because of the instability of the ion source—for example, in elemental analysis using vacuum spark ionization.

Many different types of mass-spectrographic equipment are being developed and produced in the USSR. The system of indexes that has been adopted for mass spectrometers mainly classifies the instruments not by the type of design but rather by function. The index consists of two letters (MI—isotopic mass spectrometer; MKh—for chemical analysis; MS—for physico-chemical, including structural, studies; MV—high-resolution instrument) and four numbers, the first of which indicates the method used to separate the ions by mass (1—in a homogeneous magnetic field; 2—in an inhomogeneous magnetic field; A —magnetodynamic; 5—time-of-flight; 6—radio-frequency); the second, the conditions of use (1—indicators; 2—for production monitoring; 3—for laboratory studies; 4—for special conditions); and the last two, the model number. Mass spectrometers are produced abroad by several dozen firms in the USA, Japan, the Federal Republic of Germany, Great Britain, France, and Sweden.