When I read literature about peak fitting of Raman spectra of ceramics, the authors always use Lorentzian peak profiles. Is there a particular reason for using Lorentzian peaks? I find the spectra are much easier to fit using Gaussian peaks.
After a brief search on google, I find a simple justification of it in Wikipedia....
https://en.wikipedia.org/wiki/Spectral_line_shape#cite_ref-7
It explains the source of peak shape.. and also why Lorentzian fitting is preferred..
Hope it would help.
in Raman spectrum. the curves of spectral is depend according to Lorentzian distribution. It relates to mathematical form. So if you use Gausian function to analysis the raman spectrum , then your way is incorrect. So you need to know the mathematical role of the spectral curve before decide which funtion will be used for fitting or analyze. For example, for photoluminescence spectrum, the curve is driven by gausian function. So you can fitting it by gausian function. That are all my knowledge about fitting technician. It is very important in understanding of mathematical form of the spectral curves. Because there is tie relation between math and other scienses.
Khoi is correct that Raman spectra are inherently Lorentzian in shape. However, the bands are usually broadened by the instrument optics, especially the slit, so the Raman bands you record would more easily be fitted using either mixed Gaussian/Lorentzian functions, the relative amounts of each depend on the resolution and spectrometer instrument settings. You could also use a convolution of the two (a Voigt function);
Very good question, John! Indeed, comprehending the Origin of Gaussian and/or Lorentzian Line Shapes in the solid state Raman experiment is very important for practicing spectroscopist. Obviously, pure math has only secondary meaning in this case, while quantum chemistry and physics considerations are of prime importance. Please find below an excellent explanation of the point by Michael S. Bradley. (Sorry for a lengthy excerpt, but i'm afraid it is impossible to clarify this topic just on the run)
“Quantum theory states that molecules possess well defined energy levels. Transitions between these levels, caused when molecules absorb or emit energy, therefore occurs in well defined intervals (quanta), not continuously, which gives rise to the vibrational spectrum. Thus, the absorption of energy by an isolated molecule going from a ground state to a first excited state occurs at a single, well defined, frequency.
However, most vibrating molecules exist in a bath of surrounding molecules (the environment), with which they interact. Each molecule interacts with its environment in a slightly different (and dynamic) way, and thus vibrates at a slightly different frequency. The observed line shape is the sum of these individual molecules absorbing or scattering. At equilibrium, the population of vibrational states is controlled by the Boltzmann distribution. The majority of molecules in a normal IR or Raman experiment initially are in the ground state. Some of these molecules transition to the excited state when the IR radiation or Raman laser strikes the sample. The resulting absorption (IR) or change in scattering (Raman) represents the signal seen by the instrument.
Excited state molecules rapidly return to the ground state – for vibrations, this occurs after a few picoseconds (10-12 sec). This relaxation is called the lifetime (or amplitude correlation time) τa. Initially, all of the excited molecules are vibrating together (coherently), but motion and slight differences in vibrational frequencies randomizes this over time. By analogy, coherence in a singing choir produces music, but incoherence produces chaos. The spectrometer can only “see” the molecules while they are both excited and coherently vibrating (singing). As the coherence fades (with coherence lifetime τc), the now random components interfere, and effectively cancel one another (called dephasing). Although the vibrational energy is not actually lost (the choir is still making noise), the spectrometer can not “see” it – the sum of incoherence is zero.
The effective lifetime τ is a combination of these two components, the coherence lifetime τc and the amplitude correlation time τa. There are two interesting limiting cases, when τc >> τa or τc > τa, the excited molecule relaxes before incoherence becomes severe. This is the case for solids, because the environment is not in motion. The various molecules of the solid experience a statistical distribution of environments, and the line shape takes on the bell curve or Gaussian profile. This profile has the well-known shape from statistics, with a curving (not sharp) center and wings that fall away relatively quickly.
In the second case, where τc
Thank you everyone for the helpful answers. Thank you Alexander for the quote from M. S. Bradley. I'm going to read that article now.
The article by Michael S. Bradley should not be taken (too) serious. The following statement taken from the article (Article Lineshapes in IR and Raman Spectroscopy: A Primer
) is, e.g., pure humbug:"This is the case for solids, where the environment is relatively static. Within the solid, molecules can experience a statistical distribution of environments, and the line shape takes on the bell curve or Gaussian profile"
Dispersion theory tells us that the bands of solids can be modelled with damped harmonic oscillators, which, under certain approximations, result in Lorentz-profiles. I found this fully confirmed numerous times (if you are looking for references, see e.g. https://www.researchgate.net/project/Infrared-spectroscopy-and-optics-of-anisotropic-and-randomly-oriented-materials ). A Gaussian distribution for solids is complete nonsense, as in crystalline materials you can rely on the fact that those vibrations, which can be excited, are the same in every unit cell. Not even for glasses does it make much sense to assume gaussian distributions: Article Interpretation and modeling of IR-reflectance spectra of gla...
You also should not take the presented data/spectra in the article too serious. Absorbance is not simply -lg T or -lg R. In many cases such spectra need to be corrected before the shape of bands can be investigated. See e.g. https://www.researchgate.net/project/Fast-and-reliable-Determination-of-the-true-Absorbance
Demtroeder, in his book on Laser spectroscopy describes this quite simply in terms of the resonances of an idealised, forced/driven, damped, harmonic oscillator, which has a Lorenzian lineshape, which can then be broadened to a Gaussian lineshape by environmental factors, such as collisional broadening in gases, defects or inhomogeneities in crystals etc.
https://link.springer.com/content/pdf/bfm%3A978-3-662-08260-7%2F1.pdf
Yes, the Demtroeder is in fact the only spectroscopy book I know where the origin of the Lorentz-profile is explained. The origin is indeed a classical damped harmonic oscillator model (CDHO). Lorentz himself derived it in 1906 and then introduced three different approximations from which the Lorentz-profile resulted. Given the ample use of the profile, it is instructive to note that the limits of these approximations have seemingly never been explored (in case I am wrong, please post references; thanks in advance!) until recently:
Article Quantitative Evaluation of Infrared Absorbance Spectra - Lor...
Accordingly, you are only allowed to use a Lorentz-profile for oscillators up to medium strength. Otherwise you have to employ the full CDHO model. Two things have to be said about the extension in the Demtroeder for multiple oscillators: With a small modification you can get, within the limits of the approximations, oscillator strengths, damping constants and the oscillator positions. You can even use these parameters to calculate the index of refraction function without employing the Kramers-Kronig relations - just from band fitting (you can find this also in the reference above). It is just one extra line of code.
Coming back to Raman band shapes... if you use Lorentz-profiles and you say they don't work... do you know where the limits of the Lorentz-profiles are? If not, someone should explore these limits. What about using the full CDHO model instead? Nowadays it does not make a difference in terms of computing effort in contrast to the time in which Lorentz lived...
Our article presents the spectrum of a 3% aqueous solution of hydrogen peroxide, where the characteristic band of the peroxide 877 cm-1 is very well approximated by the Lorentz function.
A.V.Kraiski, N.N.Mel’nik. Concentration dependences for parameters of low-frequency of Raman spectra in weak hydrogen peroxide aqueous solutions. Bulletin of the Lebedev Physics Institute, Moscow, 2006, v.33, №1, pp.34-40.
А.В.Крайский, Н.Н.Мельник. Концентрационные зависимости параметров низкочастотных спектров комбинационного рассеяния света слабых водных растворов перекиси водорода., Краткие сообщения по физике ФИАН, М.,2006, №1, с.42-48.
Thanks every thing, Alexander Shchegolikhin, nice explanation
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