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Particular difficulties are encountered when interpreting the spectrum of an unknown mixture of gases. The proportions of ion flow from various sources can be offset one against the other only after all the sources have been identified. In many applications in vacuum technology, one will be dealing with mixtures of a few simple gases of known identity, with atomic numbers less of than 50 (whereby the process-related gases can represent exceptions). In the normal, more complicated case there will be a spectrum with a multitude of superimpositions in a completely unknown mixture of many gas components; here a qualitative analysis will have to be made before attempting quantitative analysis. The degree of difficulty encountered will depend on the number of superimpositions (individual/a few/many).
In the case of individual super impositions, mutual, balancing of the ion flows during measurement of one and the same type of gas for several atomic numbers can often be productive.
Where there is a larger number of superimpositions and a limited number of gases overall, tabular evaluation using correction factors vis à vis the spectrum of a calibration gas of known composition can often be helpful.
In the most general case a plurality of gases will make a greater or lesser contribution to the ion flow for all the masses. The share of a gas g in each case for the atomic number m will be expressed by the fragment factor Ffm,g. In order to simplify calculation, the fragment factor Ffm,g will also contain the trans mission factor TF and the detection factor DF. Then the ion current to mass m, as a function of the overall ion currents of all the gases involved, in matrix notation, is:
The ion current vector for the atomic numbers m (resulting from the contributions by the fragments of the individual gases) is equal to the fragment matrix times the vector of the sum of the flows for the individual gases.
(in simplified notation: i = FF · I)
where im+ = ion flow vector for the atomic numbers, resulting from contributions of fragments of various individual gases
One sees that the ion flow caused by a gas is proportional to the partial pressure. The linear equation system can be solved only for the special instance where m = g (square matrix); it is over-identified for m > g. Due to unavoidable measurement error (noise, etc.) there is no set of overall ion flow I+g (partial pressures or concentrations) which satisfies the equation system exactly. Among all the conceivable solutions it is now necessary to identify set I+*g which after inverse calculation to the partial ion flows I+*m will exhibit the smallest squared deviation from the partial ion currents i+m actually measured. Thus:
This minimization problem is mathematically identical to the solution of another equation system
which can be evaluated direct by the computer. The ion current vector for the individual gases is then: