2. I get it now!In summary, to perform a Taylor Series expansion for γ in powers of β^2, keeping only the third terms, we can expand (1-β^2)^ (-1/2) in powers of β^2 and substitute 0 for x, resulting in the formula: Tf (β^2;0) = 1 + (1/2)β^2 + (3/8. In Fig. 2 n n Collect real and imaginary parts 22 njn joorr 2 Set real and imaginary parts equal Solve Eq. As the width of lines is caused by the. 2b). the formula (6) in a Lorentzian context. The collection of all lightlike vectors in Lorentzian -space is known as the light. Now let's remove d from the equation and replace it with 1. If you want a quick and simple equation, a Lorentzian series may do the trick for you. x/C 1 2: (11. where p0 is the position of the maximum (corresponding to the transition energy E ), p is a position, and. The integral of the Lorentzian lineshape function is Voigtian and Pseudovoigtian. This can be used to simulate situations where a particle. the real part of the above function (L(omega))). Both the notations used in this paper and preliminary knowledge of heavy-light four-point function are attached in section 2. Microring resonators (MRRs) play crucial roles in on-chip interconnect, signal processing, and nonlinear optics. x/D R x 1 f. If you ignore the Lorentzian for a. 1 The Lorentzian inversion formula yields (among other results) interrelationships between the low-twist spectrum of a CFT, which leads to predictions for low-twist Regge trajectories. 97. (EAL) Universal formula and the transmission function. Inserting the Bloch formula given by Eq. A. 3. This makes the Fourier convolution theorem applicable. The formula of the pseudo-Voigt function expressed by a weighted sum of Gaussian and Lorentzian functions is extended by adding two other types of peak functions in order to improve the accuracy. for Lorentzian simplicial quantum gravity. Notice that in the non-interacting case, the result is zero, due to the symmetry ( 34 ) of the spectral functions. The standard Cauchy distribution function G given by G(x) = 1 2 + 1 πarctanx for x ∈ R. We can define the energy width G as being (1/T_1), which corresponds to a Lorentzian linewidth. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. represents its function depends on the nature of the function. 8813735. 3. Similarly, other spectral lines e. Sample Curve Parameters. From analytic chemistry , we learned that an NMR spectrum is represented as a sum of symmetrical, positive valued, Lorentzian-shaped peaks, that is, the spectral components of an NMR spectrum are Lorentz functions as shown in Fig. 8 which creates a “super” Lorentzian tail. We give a new derivation of this formula based on Wick rotation in spacetime rather than cross-ratio space. The Voigt profile is similar to the G-L, except that the line width Δx of the Gaussian and Lorentzian parts are allowed to vary independently. This corresponds to the classical result that the power spectrum. % and upper bounds for the possbile values for each parameter in PARAMS. Actually, I fit the red curve using the Lorentzian equation and the blue one (more smoothed) with a Gassian equation in order to find the X value corresponding to the peaks of the two curves (for instance, for the red curve, I wrote a code in which I put the equation of the Lorentzian and left the parameter, which I am interested in, free so. Convolution of a Gaussian function (wG for FWHM) and a Lorentzian function. We will derive an analytical formula to compute the irreversible magnetization, and compute the reversible component by the measurements of the. Voigt profiles 3. M. [1-3] are normalized functions in that integration over all real w leads to unity. Lorentzian. The full width at half‐maximum (FWHM) values and mixing parameters of the Gaussian, the Lorentzian and the other two component functions in the extended formula can be approximated by polynomials of a parameter ρ = Γ L /(Γ G + Γ L), where Γ G and Γ L are the FWHM values of the deconvoluted Gaussian and Lorentzian functions,. e. M. The second item represents the Lorentzian function. • Angle θ between 0 and 2π is generated and final particle position is given by (x0,y0) = (r xcosθ,r xsinθ). Many space and astrophysical plasmas have been found to have generalized Lorentzian particle distribution functions. This section is about a classical integral transformation, known as the Fourier transformation. The coherence time is intimately linked with the linewidth of the radiation, i. The parameter Δw reflects the width of the uniform function where the. (Erland and Greenwood 2007). • Solving r x gives the quantile function for a two-dimensional Lorentzian distribution: r x = p e2πξr −1. 1. In § 3, we use our formula to fit both the theoretical velocity and pressure (intensity) spectra. g. At , . Center is the X value at the center of the distribution. square wave) require a large number of terms to adequately represent the function, as illustrated in Fig. What is now often called Lorentz ether theory (LET) has its roots in Hendrik Lorentz's "theory of electrons", which marked the end of the development of the classical aether theories at the end of the 19th and at the beginning of the 20th century. Re-discuss differential and finite RT equation (dI/dτ = I – J; J = BB) and definition of optical thickness τ = S (cm)×l (cm)×n (cm-2) = Σ (cm2)×ρ (cm-3)×d (cm). The Fourier pair of an exponential decay of the form f(t) = e-at for t > 0 is a complex Lorentzian function with equation. The normalized pdf (probability density function) of the Lorentzian distribution is given by f. Where from Lorentzian? Addendum to SAS October 11, 2017 The Lorentzian derives from the equation of motion for the displacement xof a mass m subject to a linear restoring force -kxwith a small amount of damping -bx_ and a harmonic driving force F(t) = F 0<[ei!t] set with an amplitude F 0 and driving frequency, i. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. In quantum mechanics the delta potential is a potential well mathematically described by the Dirac delta function - a generalized function. Only one additional parameter is required in this approach. 3. Lorentzian functions; and Figure 4 uses an LA(1, 600) function, which is a convolution of a Lorentzian with a Gaussian (Voigt function), with no asymmetry in this particular case. I have some x-ray scattering data for some materials and I have 16 spectra for each material. This formula can be used for the approximate calculation of the Voigt function with an overall accuracy of 0. A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. The best functions for liquids are the combined G-L function or the Voigt profile. There are six inverse trigonometric functions. 3) The cpd (cumulative probability distribution) is found by integrating the probability density function ˆ. The Lorentz model [1] of resonance polarization in dielectrics is based upon the dampedThe Lorentzian dispersion formula comes from the solu-tion of the equation of an electron bound to a nucleus driven by an oscillating electric field E. (2) It has a maximum at x=x_0, where L^' (x)=- (16 (x-x_0)Gamma)/ (pi [4 (x-x_0)^2+Gamma^2]^2)=0. However, I do not know of any process that generates a displaced Lorentzian power spectral density. Einstein equation. Unfortunately, a number of other conventions are in widespread. To a first approximation the laser linewidth, in an optimized cavity, is directly proportional to the beam divergence of the emission multiplied by the inverse of the. We now discuss these func-tions in some detail. Characterizations of Lorentzian polynomials22 3. Replace the discrete with the continuous while letting . As is usual, let us write a power series solution of the form yðxÞ¼a 0 þa 1xþa 2x2þ ··· (4. • 2002-2003, V. FWHM means full width half maxima, after fit where is the highest point is called peak point. The formula for Lorentzian Function, Lorentz ( x, y0, xc, w, A ), is: y = y0 + (2*A/PI)* (w/ (4* (x-xc)^2 + w^2)) where: y0 is the baseline offset. 7 is therefore the driven damped harmonic equation of motion we need to solve. 0In spectroscopy, the spectral lineshape is often well described by a Voigtian function, which is the convolution of a Lorentzian function and a Gaussian function. A bijective map between the two parameters is obtained in a range from (–π,π), although the function is periodic in 2π. Convert to km/sec via the Doppler formula. In Equation (7), I 0 is defined as in Equation (3), representing the integral of the Lorentzian function. 2. Mathematical derivations are performed concisely to illustrate some closed forms of the considered profile. The Lorentzian distance formula. with. Description ¶. A related function is findpeaksSGw. On the real line, it has a maximum at x=0 and inflection points at x=+/-cosh^(-1)(sqrt(2))=0. Abstract. Subject classifications. 5 H ). The Lorentzian function is normalized so that int_ (-infty)^inftyL (x)=1. X A. A = amplitude, = center, and = sigma (see Wikipedia for more info) Lorentzian Height. The formula for a Lorentzian absorption lineshape normalized so that its integral is 1 is. The Lorentzian function is given by. 3, 0. Functions that have been widely explored and used in XPS peak fitting include the Gaussian, Lorentzian, Gaussian-Lorentzian sum (GLS), Gaussian-Lorentzian product (GLP), and Voigt functions, where the Voigt function is a convolution of a Gaussian and a Lorentzian function. 1. The Fourier transform of a function is implemented the Wolfram Language as FourierTransform[f, x, k], and different choices of and can be used by passing the optional FourierParameters-> a, b option. It has a fixed point at x=0. ¶. -t_k) of the signal are described by the general Langevin equation with multiplicative noise, which is also stochastically diffuse in some interval, resulting in the power-law distribution. By default, the Wolfram Language takes FourierParameters as . Moretti [8]: Generalization of the formula (7) for glob- ally hyperbolic spacetimes using a local condition on the gradient ∇fAbstract. I'm trying to make a multi-lorentzian fitting using the LMFIT library, but it's not working and I even understand that the syntax of what I made is completelly wrong, but I don't have any new ideas. Examples. These pre-defined models each subclass from the Model class of the previous chapter and wrap relatively well-known functional forms, such as Gaussian, Lorentzian, and Exponential that are used in a wide range of scientific domains. Functions. u/du ˆ. From this we obtain subalgebras of observables isomorphic to the Heisenberg and Virasoro algebras on the. (2)) and using causality results in the following expression for the time-dependent response function (see Methods (12) Section 1 for the derivation):Weneedtodefineaformalwaytoestimatethegoodnessofthefit. 1. I did my preliminary data fitting using the multipeak package. 4) The quantile function of the Lorentzian distribution, required for particle. x 0 (PeakCentre) - centre of peak. In addition, the mixing of the phantom with not fully dissolved. (OEIS A091648). The Tauc–Lorentz model is a mathematical formula for the frequency dependence of the complex-valued relative permittivity, sometimes referred to as. Then, if you think this would be valuable to others, you might consider submitting it as. Other known examples appear when = 2 because in such a case, the surfaceFunctions Ai(x) and Bi(x) are the Airy functions. Then Ricci curvature is de ned to be Ric(^ v;w) = X3 a;b=0 gabR^(v;e a. g. What is Gaussian and Lorentzian?Josh1079. x0 x 0 (PeakCentre) - centre of peak. In other words, the Lorentzian lineshape centered at $ u_0$ is a broadened line of breadth or full width $Γ_0. Explore math with our beautiful, free online graphing calculator. Lorentzian manifold: LIP in each tangent space 4. Convolution of Two Functions. (1) and (2), respectively [19,20,12]. 2 Shape function, energy condition and equation of states for n = 9 10 19 4. Brief Description. It cannot be expresed in closed analytical form. The variation seen in tubes with the same concentrations may be due to B1 inhomogeneity effects. 3) τ ( 0) = e 2 N 1 f 12 m ϵ 0 c Γ. Probability and Statistics. *db=10log (power) My objective is to get a3 (Fc, corner frequecy) of the power spectrum or half power frequency. If you need to create a new convolution function, it would be necessary to read through the tutorial below. Multi peak Lorentzian curve fitting. The quantity on the left is called the spacetime interval between events a 1 = (t 1 , x 1 , y 1 , z 1) and a 2 = (t 2 , x 2 , y 2 , z 2) . 3) (11. , same for all molecules of absorbing species 18 3. 2iπnx/L. Function. ξr is an evenly distributed value and rx is a value distributed with the Lorentzian distribution. system. It takes the wavelet level rather than the smooth width as an input argument. Although it is explicitly claimed that this form is integrable,3 it is not. The model was tried. 5: x 2 − c 2 t 2 = x ′ 2 − c 2 t ′ 2. The parameter R 2 ′ reflects the width of the Lorentzian function where the full width at half maximum (FWHM) is 2R 2 ′ while σ reflects the width of the Gaussian with the FWHM being ∼2. For math, science, nutrition, history. As a result, the integral of this function is 1. Download scientific diagram | Fitting the 2D peaks with a double-Lorentzian function. 1. §2. Voigt (from Wikipedia) The third peak shape that has a theoretical basis is the Voigt function, a convolution of a Gaussian and a Lorentzian, where σ and γ are half-widths. Lorentzian. Recently, the Lorentzian path integral formulation using the Picard–Lefschetz theory has attracted much attention in quantum cosmology. It gives the spectral. An efficient method for evaluating asymmetric diffraction peak profile functions based on the convolution of the Lorentzian or Gaussian function with any asymmetric window function is proposed. as a basis for the. Your data really does not only resemble a Lorentzian. Download : Download high-res image (66KB)We assume that the function Λ(μ, α) is smooth, has a maximum when E μ = E α, and vanishes when E μ − E α ≫ Γ, with Γ being a typical energy width. , the three parameters Lorentzian function (note that it is not a density function and does not integrate to 1, as its amplitude is 1 and not /). Lorentz and by the Danish physicist L. A function of bounded variation is a real-valued function whose total variation is bounded (finite). The Lorentzian function has more pronounced tails than a corresponding Gaussian function, and since this is the natural form of the solution to the differential equation describing a damped harmonic oscillator, I think it should be used in all physics concerned with such oscillations, i. We describe the conditions for the level sets of vector functions to be spacelike and find the metric characteristics of these surfaces. has substantially better noise properties than calculating the autocorrelation function in equation . g. 12–14 We have found that the cor-responding temporal response can be modeled by a simple function of the form h b = 2 b − / 2 exp −/ b, 3 where a single b governs the response because of the low-frequency nature of the. curves were deconvoluted without a base line by the method of least squares curve-fitting using Lorentzian distribution function, according to Equation 2. The width of the Lorentzian is dependent on the original function’s decay constant (eta). 5) by a Fourier transformation (Fig. In the “|FFT| 2 + Lorentzian” method, which is the standard procedure and assumes infinite simulation time, the spectrum is calculated as the modulus squared of the fast Fourier transform of. Number: 4 Names: y0, xc, w, A Meanings: y0 = offset, xc = center, w = FWHM, A = area Lower Bounds: w > 0. Sep 15, 2016. "Lorentzian function" is a function given by (1/π) {b / [ (x - a) 2 + b 2 ]}, where a and b are constants. This is done mainly because one can obtain a simple an-alytical formula for the total width [Eq. While these formulas use coordinate expressions. xc is the center of the peak. In fact,. 0 license and was authored, remixed, and/or curated by Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. The resonance lineshape is a combination of symmetric and antisymmetric Lorentzian functions with amplitudes V sym and V asy, respectively. A function of two vector arguments is bilinear if it is linear separately in each argument. The formula of the pseudo-Voigt function expressed by a weighted sum of Gaussian and Lorentzian functions is extended by adding two other types of peak functions in order to improve the accuracy when approximating the Voigt profile. 000283838} *) (* AdjustedRSquared = 0. It is used for pre-processing of the background in a spectrum and for fitting of the spectral intensity. ionic and molecular vibrations, interband transitions (semiconductors), phonons, and collective excitations. In § 4, we repeat the fits for the Michelson Doppler Imager (MDI) data. τ(0) = e2N1f12 mϵ0cΓ. Lorentzian function l(x) = γ x2+ γ2, which has roughly similar shape to a Gaussian and decays to half of its value at the top at x=±γ. (2) It has a maximum at x=x_0, where L^' (x)=- (16 (x-x_0)Gamma)/ (pi [4 (x-x_0)^2+Gamma^2]^2)=0. In this article we discuss these functions from a. This is not identical to a standard deviation, but has the same. Lorentzian functions; and Figure 4 uses an LA(1, 600) function, which is a convolution of a Lorentzian with a Gaussian (Voigt function), with no asymmetry in this particular case. The derivative is given by d/(dz)sechz. Note that the FWHM (Full Width Half Maximum) equals two times HWHM, and the integral over the Lorentzian equals the intensity scaling A. The mathematical community has taken a great interest in the work of Pigola et al. Δ ν = 1 π τ c o h. . In particular, we provide a large class of linear operators that. To do this I have started to transcribe the data into "data", as you can see in the picture:Numerical values. e. Here δt, 0 is the Kronecker delta function, which should not be confused with the Dirac. x/D 1 1 1Cx2: (11. 7 is therefore the driven damped harmonic equation of motion we need to solve. Jun 9, 2017. 1cm-1/atm (or 0. Lorentzian line shapes are obtained for the extreme cases of ϕ→2nπ (integer n), corresponding to. Caron-Huot has recently given an interesting formula that determines OPE data in a conformal field theory in terms of a weighted integral of the four-point function over a Lorentzian region of cross-ratio space. The Lorentzian function is encountered. Wells, Rapid approximation to the Voigt/Faddeeva function and its derivatives, Journal of Quantitative. Valuated matroids, M-convex functions, and Lorentzian. The constant factor in this equation (here: 1 / π) is in. Function. The response is equivalent to the classical mass on a spring which has damping and an external driving force. For the Fano resonance, equating abs Fano (Eq. g(ν) = [a/(a 2 + 4π 2 ν 2) - i 2πν/(a 2. The equation of motion for a harmonically bound classical electron interacting with an electric field is given by the Drude–Lorentz equation , where is the natural frequency of the oscillator and is the damping constant. 2 Mapping of Fano’s q (line-shape asymmetry) parameter to the temporal response-function phase ϕ. 5. g. CHAPTER-5. 1. It is an interpolating function, i. The main property of´ interest is that the center of mass w. In particular, is it right to say that the second one is more peaked (sharper) than the first one that has a more smoothed bell-like shape ? In fact, also here it tells that the Lorentzian distribution has a much smaller degree of tailing than Gaussian. 3. (5)], which later can be used for tting the experimental data. This is compared with a symmetric Lorentzian fit, and deviations from the computed theoretical eigenfrequencies are discussed. 1 2 Eq. Equation (7) describes the emission of a plasma in which the photons are not substantially reabsorbed by the emitting atoms, a situation that is likely to occur when the number concentration of the emitters in the plasma is very low. In fact, all the models are based on simple, plain Python functions defined in the lineshapes module. The pseudo-Voigt function is often used for calculations of experimental spectral line shapes . Eqs. Its Full Width at Half Maximum is . Graph of the Lorentzian function in Equation 2 with param- eters h = 1, E = 0, and F = 1. The Pearson VII function is basically a Lorentz function raised to a power m : where m can be chosen to suit a particular peak shape and w is related to the peak width. 5. I have a transmission spectrum of a material which has been fit to a Lorentzian. Methods: To improve the conventional LD analysis, the present study developed and validated a novel fitting algorithm through a linear combination of Gaussian and Lorentzian function as the reference spectra, namely, Voxel-wise Optimization of Pseudo Voigt Profile (VOPVP). This plot shows decay for decay constant (λ) of 25, 5, 1, 1/5, and 1/25 for x from 0 to 5. e. Figure 2: Spin–orbit-driven ferromagnetic resonance. 4. Delta potential. The derivation is simple in two. lorentzian function - Wolfram|Alpha lorentzian function Natural Language Math Input Extended Keyboard Examples Compute answers using Wolfram's breakthrough. It is implemented in the Wolfram Language as Sech[z]. A is the area under the peak. Its Full Width at Half Maximum is . 3. The formula for Lorentzian Function, Lorentz(x, y0, xc, w, A), is: . The Lorentzian distance formula. This functional form is not supplied by Excel as a Trendline, so we will have to enter it and fit it for o. It is often used as a peak profile in powder diffraction for cases where neither a pure Gaussian or Lorentzian function appropriately describe a peak. Figure 2 shows the influence of. The corresponding area within this FWHM accounts to approximately 76%. The formula was obtained independently by H. Valuated matroids, M-convex functions, and. (3) Its value at the maximum is L (x_0)=2/ (piGamma). Expansion Lorentz Lorentz factor Series Series expansion Taylor Taylor series. 0 for a pure. However, only three integration formulas are noted in the rule on integration formulas resulting in inverse trigonometric functions because the remaining three are negative versions of the ones we use. It is the convolution of a Gaussian profile, G(x; σ) and a Lorentzian profile, L(x; γ) : V(x; σ, γ) = ∫∞ − ∞G(x ′; σ)L(x − x ′; γ)dx ′ where G(x; σ) = 1 σ√2πexp(− x2 2σ2) and L(x; γ) = γ / π x2 + γ2. As the damping decreases, the peaks get narrower and taller. Brief Description. This chapter discusses the natural radiative lineshape, the pressure broadening of spectral lines emitted by low pressure gas discharges, and Doppler broadening. Max height occurs at x = Lorentzian FWHM. e. n. Linear operators preserving Lorentzian polynomials26 3. e. Download scientific diagram | Lorentzian fittings of the spectra in the wavenumber range from 100 to 200 cm À1 for the TiO 2 films doped with (a) 15% boron and (b) 20% boron. Lorentzian distances in the unit hyperboloid model. 19e+004. 4 illustrates the case for light with 700 Hz linewidth. 9: Appendix A- Convolution of Gaussian and Lorentzian Functions is shared under a CC BY-NC 4. If η decreases, the function becomes more and more “pointy”. A representation in terms of special function and a simple and. According to the literature or manual (Fullprof and GSAS), shall be the ratio of the intensities between. % and upper bounds for the possbile values for each parameter in PARAMS. Our method calculates the component. 1 Landauer Formula Contents 2. pdf (y) / scale with y = (x - loc) / scale. Publication Date (Print. ferential equation of motion. . 0451 ± 0. It is typically assumed that ew() is sufficiently close to unity that ew()+ª23 in which case the Lorentz-Lorenz formula simplifies to ew p aw()ª+14N (), which is equivalent to the approximation that Er Er eff (),,ttª (). ionic and molecular vibrations, interband transitions (semiconductors), phonons, and collective excitations. Tauc-Lorentz model. In fact, the distance between. Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more. Drude formula is derived in a limited way, namely by assuming that the charge carriers form a classical ideal gas. Sample Curve Parameters. This function returns four arrays, Ai, Ai0, Bi, and Bi0 in that order. 2, and 0. Equations (5) and (7) are the transfer functions for the Fourier transform of the eld. This is not identical to a standard deviation, but has the same. The specific shape of the line i. The script TestPrecisionFindpeaksSGvsW. Graph of the Lorentzian function in Equation 2 with param- ters h = 1, E = 0, and F = 1. 15/61formulations of a now completely proved Lorentzian distance formula. CEST generates z-spectra with multiple components, each originating from individual molecular groups. GL (p) : Gaussian/Lorentzian product formula where the mixing is determined by m = p/100, GL (100) is. We then feed this function into a scipy function, along with our x- and y-axis data, and our guesses for the function fitting parameters (for which I use the center, amplitude, and sigma values which I used to create the fake data): Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. The computation of a Voigt function and its derivatives are more complicated than a Gaussian or Lorentzian. Instead of using distribution theory, we may simply interpret the formula. These pre-defined models each subclass from the Model class of the previous chapter and wrap relatively well-known functional forms, such as Gaussian, Lorentzian, and Exponential that are used in a wide range of scientific domains. Please, help me. The combined effect of Lorentzian and Gaussian contributions to lineshapes is explained. This is because the sinusoid is a bounded function and so the output voltage spectrum flattens around the carrier. m which is similar to the above except that is uses wavelet denoising instead of regular smoothing. We show that matroids, and more generally $\mathrm {M}$-convex sets, are characterized by the Lorentzian property, and develop a theory around Lorentzian polynomials. . Homogeneous broadening. Note the α parameter is 0. Guess 𝑥𝑥 4cos𝜔𝑡 E𝜙 ; as solution → 𝑥 ä Lorentzian, Gaussian-Lorentzian sum (GLS), Gaussian-Lorentzian product (GLP), and Voigt functions. The real spectral shapes are better approximated by the Lorentzian function than the Gaussian function. The experimental Z-spectra were pre-fitted with Gaussian. By supplementing these analytical predic- Here, we discuss the merits and disadvantages of four approaches that have been used to introduce asymmetry into XPS peak shapes: addition of a decaying exponential tail to a symmetric peak shape, the Doniach-Sunjic peak shape, the double-Lorentzian, DL, function, and the LX peak shapes, which include the asymmetric Lorentzian (LA), finite. which is a Lorentzian function. 544. That is, the potential energy is given by equation (17. In other words, the Lorentzian lineshape centered at $ u_0$ is a broadened line of breadth or full width $Γ_0. The graph of this equation is still Lorentzian as structure the term of the fraction is unaffected. It should be noted that Gaussian–Lorentzian sum and product functions, which approximate the Voigt function, called pseudo-Voigt, have also been widely used in XPS peak fitting. When i look at my peak have a FWHM at ~87 and an amplitude/height A~43. 2. Try not to get the functions confused.