### Project Description

**Abstract**

Mass spectrometry is a method of analysis that permits to quantify the composition of gaseous mixtures. Nevertheless, a disadvantage of low resolution mass spectrometers, like most commercial type quadrupole instruments, is the difficulty to identify and to determine the gases and their partial pressures respectively because of spectral overlap (as an example N_{2} and CO have the base peak at the same mass number 28).

A method for quantitative analysis is here presented; from the measured ion currents and the gas cracking patterns (that may be obtained by previous gas calibrations) the following procedures are executed: 1) identification of the gases which are present in the vacuum system; 2) determination of their partial pressures.

The method has been tested by known gaseous mixtures of N_{2} and CO and using a quadrupole as analyzer. A computer program for quantitative analysis, which runs on personal computers, has been developed; it accesses to common in use spreadsheet softwares for data input and output.

**Riassunto**

La spettrometria di massa è un metodo di analisi che permette la identificazione e quantificazione della composizione di miscele gassose. Tuttavia, un grosso svantaggio nei spettrometri a bassa risoluzione, come gran parte dei quadrupoli in commercio, è la difficoltà di dedurre i gas presenti nel sistema e le loro pressioni parziali in quanto gli spettri caratteristici dei singoli gas presentano picchi sovrapposti (tipico esempio N_{2} e CO entrambi con picchi fondamentali alla massa 28).

Un metodo di analisi quantitativa è qui presentato. Partendo dalle correnti ioniche misurate e dai rapporti di frammentazione dei singoli gas (che possono essere determinati da preliminari calibrazioni), vengono eseguite le seguenti procedure: 1) identificazione dei gas presenti nel sistema; 2) calcolo delle loro pressioni parziali.

Tale metodo è stato collaudato con miscele di gas note contenenti N_{2} e CO e usando un quadrupolo come analizzatore. Un programma di calcolo per l’analisi quantitativa e utilizzabile su un personal computer, è stato sviluppato; esso utilizza diffusi programmi a fogli elettronici per l’ingresso e produzione dei dati.

### 1. Introduction

Mass spectrometry is a widespread technique for accurate and quick analysis of the composition of the gaseous mixture which it is present in a vacuum system.

It has a wide range of applications: in process monitoring and control, in laboratory analysis and research. When linked to a gas-liquid chromatograph, it provides a powerful tool for identifying a large number of compound which may be present also in extremely small quantities.

Although mass spectrometry has been recognized as a technique for quantitative analysis since its inception, the interpretation and quantification of the mass spectra are not straightforward for two principal reasons:

- the number of peaks generated by a single gas are more than one (peaks fragmentation);
- the peaks of different gases may overlap at some characteristics fragment mass numbers (spectral overlap), making often difficult their distinction.

A solution to these problems is given by high-resolution mass spectrometers (resolving power larger than 1000) which resolve very close peaks (e.g. ions of N_{2}^{+} and CO^{+} at mass numbers 28.0061 and 27.9949 respectively). However their high cost (and high dimension) restrict the use in few selected analytical laboratories.

Low-resolution spectrometers (resolving power from 100 to 1000), like quadrupole instruments, are, on the contrary, very popular since they are relatively inexpensive, compact and need little experience and training to operate. Because of their limited mass resolution, these spectrometers cannot eliminate the spectral overlap and the distinction between gases can be appraised by looking at the secondary peaks of their fragmentation. As a matter of fact, the peaks fragmentation becomes a great help for mass spectra analysis since the peaks which are generated by a gas are unique for this gas, like a fingerprint.

As an example, N_{2} and CO are both detected, by a low-resolution mass spectrometer, at the mass number 28 (the “parent” ions N_{2}^{+} and CO^{+} respectively), therefore the gases may be distinguished by a comparison of the secondary peaks at specific mass numbers: 14 ( N^{+} , CO^{++}), 29 ( ^{15} N ^{14} N^{+} , ^{13} C ^{16} O^{+} ), 12 ( C^{+} ) and 16 ( O^{+} ).

The quantitative analysis of a mass spectrum involves two steps:

- identification of the gas components in the mixture (as in qualitative analysis);
- evaluation of the partial pressures of the gases identified at step 1).

The second step can be solved, in a simple way, if the mass spectrum of the gaseous mixture is a linear combination of the mass spectra of its gas components. Therefore a reliable quantitative analysis requires a high linearity (linear relationship between gas partial pressures and the detected ion currents) of the spectrometer instrument. In this condition the evaluation of the partial gas pressures becomes simple by means of linear regression techniques.

A lot of computer programs [1,2] (sometimes supplied by the mass spectrometer manufacturer as a companion software for mass spectra acquisition and analysis), are available for the calculation of the gas partial pressures or gas concentrations with a given and fixed set of gases (that is only the step 2 is solved). The novelty of the method, here described, for quantitative analysis, is the inclusion of an initial statistical procedure for the identification of the gas components in the mixture (step 1).

According to this method, at the beginning a (large) set of gases which are suspected to be present in the mixture is chosen then a statistical test selects the subset of gases which “best” reproduce the observed mass spectrum.

In the following, the procedures for quantitative analysis will be described and the main specifications for reliable quantitative analysis will be also shown. An application concerning the identification of N_{2} / CO mixtures will be presented. The method for quantitative analysis, here described, has been developed into a computer program compatible with a personal computer.

### 2. Basic Principles for Quantitative Analysis

The quantitative analysis of a gaseous mixture by means of a mass spectrometer is based on the relationship between the ion currents, I_{i} , which are observed at different specific mass numbers (ratio mass to charge), M_{i} , and the partial pressures, P_{k} , of the gases G_{k} , which are present in the mixture [3]:

where i and k are integer index for the ion currents and the gases respectively ( 1< i < n_{m} , 1< k < n_{g} where n_{m} and n_{g} are the number of the measured ion currents and of the gases respectively); S_{ik} are the instrument’s sensitivities for the gas G_{k} at the peak corresponding to the specific mass number M_{i} , namely S_{ik} = S(M_{i} , G_{k}) .

The gas sensitivities depend on the atomic-molecular reactions which occur in the ionizing source of the mass spectrometer due to the electron collisions with the gas molecules; the results is the fragmentation of the gas molecules into ions of different masses. The relative fractions of the fragment ions (so-called cracking patterns) depend essentially on the electron energy (that for most quadrupoles is between 70 eV and 100 eV). A fraction of the ions produced in the source are then drawn out to the analyzer (mass filter); it follows that further influences to the sensitivities are due to the instrument’s transmission factors between the different elements of the mass spectrometer (from the source to the analyzer and from the analyzer to the detector) [4].

The sensitivities are generally constant by changing gas pressure, therefore, according to eq.(1), there is a linear relationship between partial gas pressures and the detected ion currents (the pressure range of linearity is a basic specification for a mass spectrometer and it is essential in quantitative analysis[4]).

However towards high gas pressure (close to the maximum operating pressure of the instrument, which for most quadrupoles is between 10^{-4} and 10^{-3} mbar), the high ion production rate determines space charge effects and gas collisions; in this pressure region the sensitivities cease to be constant with changing pressure [5]. Other possible sources of error in mass spectrometry which could lead to misleading interpretation of the mass spectra are given in [6].

### 2.1 A Simple Method for Gas Calibration

The quantitative evaluation of the gas partial pressure from the observed ion currents (eq.1) requires the knowledge of the sensitivities S_{ik} at least for those gases of main concern in the laboratory applications. Being the sensitivities typical of the instrument, their in-situ determination (gas calibration) is highly recommended. As a simple and direct method, the calibrating gas, G_{k} , is fed into a volume connected to the mass spectrometer; from the measured ion currents, I_{i} , corresponding to the gas cracking pattern, the sensitivities are obtained by eq.(1) which for a single gas becomes: S_{i k} = I_{i} / P_{k} . The (total) gas pressure P_{k} is obtained by means of a gauge head (e.g. a Bayard-Alpert) with the measured pressure corrected with the ionization factor for the gas (provided by the gauge manufacturer); at high pressures, from 10^{-5} to 10^{-3} mbar, the spinning-rotor gauge can provide a more precise pressure measurement. More accurate methods for gas calibration of mass spectrometer for quantitative gas analysis are given in [7].

The plot of the ion currents versus the gas pressure provides a method to determine the pressure range of the linearity of the mass spectrometer (in general the ion gauges for total pressure are much more linear and stable respect to most of the mass spectrometers [5]).

### 2.2 Gas Partial Pressures Evaluation

In the linearity range of the mass spectrometer, the relationship (1) represents a system of n_{m} linear equations in n_{g} unknowns (the gas partial pressures P_{k} ). Since most gases have more than one peak, then n_{m} < n_{g} and the system (1) becomes overspecified; in this case the system (1) represents a multiple linear regression model.

Least squares is the most viable principle to apply for estimation of the regression parameter (the partial gas pressures). According to this principle, the parameters are estimated in such a way to minimize the residual sum of squares, that is the sum of squared departures (differences between the observed values of the dependent variable, the ion currents, and the values predicted by the regression equations, RHS of eq.(1) ).

The computational algorithm use the factorization of the matrix S_{ik} into simpler matrices (triangular and orthogonal matrices), commonly referred as QR factorization; this method produces more accurate solutions than those obtained from traditional methods based on the normal equations [8].

### 2.3 The Identification of the Gas Components

A statistical technique [9] is used for making a decision whether or not a gas component is present in the gaseous mixture. At first a (large) initial set of gases which are suspected to be present in the gaseous mixture is selected by means of a general (or qualitative) analysis of the measured peak values in the mass spectrum; besides it is fixed a critical confidence level (e.g. 95 % ) for a gas of the initial set to enter in the gaseous mixture. The statistical procedure determines in a sequential way the subset of the gases which are the most probable in the gaseous mixture. Practically the subset is systematically build up by adding one by one a gas from the initial set (forward selection procedure); at each step, the gas of the initial set and that it has not been selected in the previous steps, which gives the smallest residual sum of squares (namely the “best fitting gas”) is selected for the statistical test (F-test). If the test for this gas gives an observed confidence level greater than the chosen critical confidence level, the gas is included in the final subset, otherwise the gas is excluded and the overall procedure stops (the inclusion of any of the remaining gases gives ever an observed confidence level smaller respect to the fixed level).

The result of the statistical procedure is the “best” subset of the regression parameters (partial gas pressures) for modeling the observed values of the independent variables (ion currents) according to the linear regression equations (1) and with a larger confidence respect to the fixed level.

### 3. Application of Quantitative Gas Analysis

The procedures here developed for the evaluation of mass spectra have been tested with known gaseous mixtures of N_{2} and CO and using a quadrupole as mass analyzer. These mixtures have been chosen because of the presence of many common peaks in their mass spectra (see Section 1), thus for the determination of their gas compositions complications should be expected.

The experimental apparatus consists of a test volume which houses the quadrupole analyzer (Balzers QMS 125) and the Bayard-Alpert gauge for total pressure measurement. The volume and a turbomolecular pumping system are connected by a gate valve of high conductance. The base gas pressure in the volume after baking for 24 hours at 250 C was less than 10^{-9} mbar and consisted mainly of hydrogen and smaller amounts of H_{2} O , CO and CO_{2} .

An experimental run begins by introducing the mixture into the volume by means of a variable leak valve and with the gate valve open. Then a continuous gas flow is established by adjusting the leak valve and/or the gate valve in such a way to maintain a steady gas pressure in the volume.

Table 1: Measured cracking patterns and their standard errors for N_{2} , CO , CO_{2} and CH_{4} . Base peak (b.p.) normalized to 100.

mass number |
N_{2} |
CO |
CO_{2} |
CH_{4} |

12 | 2.8 ±0.2 | 6.6 ±0.4 | 2.9 ±0.4 | |

13 | 6.9 ±0.5 | |||

14 | 9.7±0.1 | 1.0 ±0.1 | 19.0 ±1.0 | |

15 | 87.0 ±0.5 | |||

16 | 0.8 ±0.1 | 12.3 ±0.4 | 100 | |

22 | 2.6 ±0.4 | |||

28 | 100 | 100 | 10.2 ±0.4 | |

29 | 0.9±0.1 | 1.2 ±0.2 | ||

44 | 100 | |||

45 | 1.3 ±0.1 | |||

sensitivity for b.p. | ||||

( 10^{-4} A/mbar) |
2.0 ±0.1 | 2.3 ±0.1 | 1.8 ±0.2 | 1.6 ±0.2 |

Several measurements have been performed with pure gases and gaseous mixtures at different pressures between 10^{-7} and 5 10^{-5} mbar; with the lower limit being set to avoid the contribution of the background gas in the volume and the higher limit because the gas sensitivities start to be pressure dependent. Before each set of measurements (run) with a gas, the background spectrum (with closed leak valve and open gate valve) is recorded and subtracted from the successive mass spectra.

The instrument’s gas sensitivities, S_{ik} , for the (pure) gases of interest N_{2} , CO and in addition for CO_{2} and CH_{4} (of which mass spectra contain minor peaks overlapping with the peaks of N_{2} and CO ) have been determined according to the method indicated in Section 2.1. Table I lists the measured cracking patterns of these gases; the convention to normalize the base peak (relative to the parent ion) to 100 has been used. The measured ion currents of the gaseous mixture, the cracking patterns values (Table I), a critical confidence level of 95 % are the input data for the procedures of gas identification and partial pressures calculation. The statistical procedure selects correctly the gas components ( N_{2} and CO ) of the gaseous mixtures (only a much lower confidence level should allow the entry of CO_{2} and CH_{4} but their calculated fractions should be much lower respect to the calculated ones of the principal gases).

In Table II the certified values of the gaseous mixtures (supplier: Sapio-Milano) are compared with those obtained by the proposed procedures. The total pressures, calculated from the evaluated partial pressures, P_{k} , namely

, have relative deviations respect to the measured total pressures ( P_{BA} ) lower than 5 % (n.b. P_{BA} have been corrected with the instrument’s gas ionization factors weighted according to the certified values of the gas concentrations in the gaseous mixture).

The calculated gas concentrations, C_{k} = P_{k} / P_{T} , agree well with the certified values and the range given by calculated standard errors covers the certified values of all the gases. The deviations between the calculated concentrations respect to the certified values are within ±1 % in concentration and in relative scale lower than 5 % in all cases and lower than 1 % when N_{2} and CO concentrations are similar (mixture 2).

Table 2: Comparison of certified values (c.v.) and evaluated gas concentrations ( C_{N2} and C_{CO} ) from the mass spectra of known gaseous mixtures (m.) measured at different pressures (run); the departures from the c.v. concentrations of N_{2} are given by: d(N_{2})=C_{N2} (c.v.)-C_{N2} .

m. |
run |
P_{BA}10 ^{-6} mbar |
P_{T}10 ^{-6} mbar |
C_{N2 }% |
C_{CO }% |
d(N_{2})% |

1 | c.v. | 89.7 ±0.2 | 10.3 ±0.2 | |||

1 | 1 | 0.60 | 0.63 ±0.05 | 89.5 ±3.0 | 10.5 ±1.2 | +0.2 |

1 | 2 | 1.5 | 1.6 ±0.1 | 89.1 ±2.7 | 10.9 ±1.0 | +0.7 |

1 | 3 | 6.7 | 6.6 ±0.1 | 89.8 ±1.7 | 10.2 ±0.6 | -0.1 |

1 | 4 | 15 | 15 ±1 | 89.7 ±1.3 | 10.3 ±0.4 | +0.0 |

1 | 5 | 65 | 63 ±1 | 90.1 ±0.9 | 9.9 ±0.3 | -0.3 |

2 | c.v. | 48.8±1.0 | 51.2 ±1.0 | |||

2 | 1 | 0.57 | 0.60 ±0.05 | 49.7 ±2.9 | 50.3 ±2.8 | -0.9 |

2 | 2 | 1.5 | 1.6 ±0.1 | 48.8 ±2.6 | 51.2 ±2.6 | +0.0 |

2 | 3 | 6.5 | 6.3 ±0.2 | 48.8 ±1.8 | 51.2 ±1.8 | -0.0 |

2 | 4 | 15 | 14 ±1 | 48.8 ±2.0 | 51.2 ±2.0 | +0.0 |

2 | 5 | 64 | 62 ±2 | 49.4 ±0.8 | 50.6 ±1.0 | +0.6 |

3 | c.v. | 11.3 ±1.8 | 88.7 ±1.8 | |||

3 | 1 | 0.64 | 0.68 ±0.05 | 11.9 ±2.1 | 88.1 ±2.6 | -0.6 |

3 | 2 | 1.4 | 1.5 ±0.1 | 11.6 ±1.4 | 88.4 ±2.4 | -0.3 |

3 | 3 | 6.1 | 6.4 ±0.1 | 10.9 ±0.3 | 89.1 ±0.7 | +0.4 |

3 | 4 | 14 | 13 ±1 | 10.0 ±2.0 | 90.0 ±2.2 | +1.3 |

3 | 5 | 62 | 64 ±1 | 11.6 ±1.2 | 88.4 ±1.9 | -0.3 |

### 4. A Program for Quantitative Gas Analysis

The procedures here described have been developed into a computer program, a simple version has been compiled as Microsoft Excel macro in order to use the Excel sheets for input and output.

The input data for the program are supplied in two (Excel) sheets:

- the “spectra” sheet is a mass spectral database, with the cracking patterns and sensitivity for the base peak of different gases. The user can modify or expand the content of the spectra library by in-situ gas calibrations, or in alternative by importing the cracking pattern as supplied by the mass spectrometer manufacturer or from other sources available in literature or commercially (e.g. the NIST Mass Spectral Library [10];
- in the “ion currents” sheet the ion currents measured at different mass numbers, M
_{i}, are entered. A cell corresponds to the ion current relative to M_{i}and to a time cycle. A lot of data acquisition softwares, usually supplied by the instrument manufacturer, allow to import the acquired data into an Excel sheet.

The user enters the symbols of the gases (they must be present in the spectra library too) that he suspects to be contributing to the measured spectra at the different cycles. By default the program starts with the gas identification procedure and selects for each cycle the subset of gases according to the statistical method of Section 2.3 . Afterwards, the regression procedure (Section 2.2) calculates the partial pressures of the selected gases together with an estimate of their standard errors. The values of the partial pressures and the standard errors are displayed and recorded in the “ion currents” sheet.

The user has the possibility to modify the gas selection procedure by changing the critical confidence level (default 95 % ) or by forcing the inclusion (or exclusion) of some gases in the final subset.

### 5. Conclusions

The quantitative analysis (QA) of mass spectra to determine the gas composition in a vacuum system can be performed with a commercial type (low resolution) mass spectrometer, as the quadrupole instrument. There are two main demands for reliable QA:

- instrument linearity, the gas sensitivities must remain quite constant over a large pressure range;
- knowledge of the instrument’s sensitivities at least for the gases of main interest; the best way is their determination by in-situ gas calibrations.

In these conditions, the partial gas pressures can be determined from the measured ion currents and a good accuracy can be achieved also in the case of spectral overlap among gases.

The proposed procedures for QA not only solve the problem of the partial pressures evaluation but identify, by means of a statistical test, the gases in the vacuum system.

These procedures have been tested on gaseous mixtures having an high spectral overlap; the evaluation of the measured spectra gives reliable results with typical errors of about 1 % and lower than 5 % in all cases.

A computer program has been written, it includes the indicated procedures for QA and works in a Microsoft Excel environment.

**Reference**

[1] R. Dobrozemsky, J. Vac. Sci. Technol., 9,220 (1972).

[2] W. K. Schorr, H. Duschner and K. Starke, Anal. Chem., 54,671 (1982)

[3] J. F. O’Hanlon, *A User’s Guide to Vacuum Technology*, John Wiley & Sons, New York, ch.4 (1980).

[4] W. Große Bley, Vacuum,38,103 (1988).

[5] L. Lieszkovszky, A. R. Filippelli and C. R. Tilford, J. Vac. Sci. Technol.,A 8, 3838 (1990).

[6] P. H. Dawson (editor), *Quadrupole Mass Spectrometry and its Applications*, Elsevier, Amsterdam, (1976)

[7] R. E. Ellefson, D. Cain and C. N. Lindsay, J. Vac. Sci. Technol.,A 5,134 (1987).

[8] D. Kahaner, C. Moler and S. Nash, *Numerical Methods and Software*, Prentice-Hall, Englewood Cliffs (NJ,USA), ch. 6 (1989).

[9] N. R. Draper, H. Smith, *Applied Regression Analysis*, John Wiley & Sons, New York, ch. 15 (1998).

[10] *NIST/EPA/NIH Mass Spectral Library*. Documentation available electronically via: http://www.nist.gov/srd/analy.htm.

**
G. Gervasini
**Istituto di Fisica del Plasma, Consiglio Nazionale delle Ricerche – Associazione EURATOM-ENEA-CNR – Via Cozzi 53, 20125 Milano (Italy)