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The photoelectrons then travel through a spectrometer that broadens the signal to some degree. There will be some line width to the X-rays that excite the photoelectrons, e.g., they won’t be perfectly monochromatic. However, there are many reasons why this natural line shape will not be exactly observed. In the theory of X-ray photoelectron spectroscopy, natural line shapes are generally assumed to be Lorentzian. Any serious physical scientist should know the difference between these two functions and be comfortable working with them. The Lorentzian is a little more peaked, i.e., a little narrower around its maximum, and it extends out a little more than the Gaussian on its sides, i.e., the Lorentzian has ‘wings’. The Gaussian curve is the classic ‘bell-shaped curve’. They also have finite integrals and are localized – they do not have large tails or other components that extend out to a significant degree. Obviously, both functions are symmetric about the y-axis. These functions are graphed in Figure 1 (the Gaussian) and Figure 2 (the Lorentzian) with the following parameters: h = 1 (the functions are given here a height of one), E = 0 (the functions are centered at the origin), and F = 1 (the functions have a width of one). The general forms of these functions, including their sum and product functions, have previously appeared a number of times in the literature.5 (1) Their general mathematical forms are given in Equations 1 and 2, respectively. Gaussian and Lorentzian functions play an important role in science. Gaussian-Lorentzian sum function (GLS), and the Gaussian-Lorentzian product (GLP) function. The most common functions chosen to represent symmetric XPS signals are the Voigt function, which is the convolution of a Gaussian function with a Lorentzian function, the
#Xps peak fitting gaussian lorentzian series
XPS Peak Fitting with Voigt and Gaussian-Lorentzian Sum and Product Functions In peak fitting an XPS narrow scan, one generally selects a baseline first followed by a series of peaks, where each peak will, in general, represent a single chemical state (oxidation state1) of an element. Graph of the Lorentzian function in Equation 2 with parameters h = 1, E = 0, and F = 1.
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Graph of the Gaussian function in Equation 1 with parameters h = 1, E = 0, and F = 1.įigure 2. We’ll discuss these three functions in this article, and then move on to the impulse function, which I believe is an interesting piece of mathematics that any scientist or engineer should be familiar with.įigure 1. Ian-Lorentzian sum function (GLS), and the Gaussian-Lorentzian product (GLP) function. The most widely used functions for fitting peaks in XPS narrow scans are based on Gaussian and Lorentzian functions, and three such functions are regularly considered for this purpose: the Voigt function, which is the convolution of a Gaussian function with a Lorentzian function (we considered convolution in the last column4), the Gauss. Sherwood aptly observed that peak fitting in XPS is commonly practiced because forms of the same element in different oxidation states1 often yield signals that are separated by about as much as their line widths.1-2 Crist has observed that important decisions in the laboratory and in industry are regularly based on the results from peak fitting.3 I have found all of this to be true. N this column I’ll be talking about a nearly unavoidable, and certainly indispensible, part of X-ray photoelectron spectroscopy (XPS): peak fitting of narrow scans. The Gaussian-Lorentzian Sum, Product, and Convolution (Voigt) Functions Used in Peak Fitting XPS Narrow Scans, and an Introduction to the Impulse Function The G component may be due to nitrogen trapped at defects.By Matthew R. The origins of these components are discussed. The intensity of the D component was always comparable to that of the F component in both diamond and graphite cases. The splitting is caused by evaporation of the volatile E component (∼399.7 eV). The broad N1s XPS peak at ∼400 eV splits clearly into the D (∼398.4 eV) and F (∼401.2 eV) components upon annealing at 600☌ in vacuum. The C component at ∼287.3 eV is attributed to genuine nitrides such as C 3N 4. The B component at ∼286.0 eV originates in the damaged phase and the sub-nitride phase (CN x: x<1). The A component at ∼284.8 eV is assigned to the non-damaged substrate below the ion penetration depth. The XPS spectra of C1s and N1s core levels are divided into three (A, B, C) and four (D, E, F, G) components, respectively. X-ray photoelectron spectra (XPS) were recorded in situ during the nitridation.
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Diamond (CVD) and graphite (HOPG) samples were nitrided at room temperature by irradiation with 300–700 eV N 2 + ion beams.