# Accounting for Interelement Interferences in Atomic Emission Spectroscopy: A Nonlinear Theory
###### Abstract
When analyzing substances using the method of evaporation from a graphite electrode, there is an effect on elements with a boiling point lower than that of carbon on the intensity of analytical lines of other impurities, which is caused by a decrease in the rate of entry of sample atoms into the discharge zone [41; 42] with an increase in the concentration of such elements. To factor in the influence of third elements on experimental data, various methods are used [43]:  
* mathematical methods for calculating corrections;
* methods that adjust the procedure of measuring the analytical signal;
* methods optimizing the process of measuring the analytical signal;
* spectrum transformation methods (Fourier transform, the differentiation of spectra, etc.). Calculating corrections is the most convenient method that does not involve making changes to the sample preparation procedure, experimental conditions, the optical arrangement of the equipment, or optical materials. However, the existing mathematical methods have a number of disadvantages. The biggest one is that the relationship between the corresponding correction and the concentration (or, in other modifications, the intensity of the analytical line) of the influencing element and the analyte (see Formula (A4) in Appendix A) [44; 45; 46; 47; 48] is assumed to be linear. When considering the complexity of the physicochemical processes that occur during the emission of impurity and alloying element atoms from the substance being analyzed (crystal structure rearrangement, diffusion, melting, evaporation, explosive emission, etc. ), and the complexity of the processes that determine the dependence of plasma parameters (if plasma is used for optical excitation) on the composition of the plasma gas, it becomes obvious that the assumed linear relationship does not correspond to the real one and, in the general case, can only give a qualitative (and only to some extent quantitative) description of the observed effects caused by third elements. In [49], it is noted that today the problem of factoring in the effects produced by third elements has no solution in the general case. The above means that when calibrating spectrometers for analyzing substances that contain impurities and alloying elements whose concentrations fluctuate over a wide range (two to four orders of magnitude), it is necessary to set different excitation and atomization parameters, i.e., to develop analytical techniques specifically for relatively small groups of alloys. For example, when analyzing low-alloy, high-speed, and high-alloy steels by means of spark spectrometers, it is necessary to adjust the parameters of the spark generator and the registration system and use different analytical and reference lines. However, when the effects caused by third elements are adequately corrected for, only one technique can be used. This obviously saves time and material resources in the production of spectrometers. Thus, it is of importance to develop a method for factoring in the effects caused by third elements that will adequately describe their influence on the results of AES experiments.