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Quantitative analysis of Raman spectral parameters for carbon fibers: practical considerations and connection to mechanical properties

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Abstract

Although the literature on the Raman spectra of carbon fibers is vast, no consistent, robust predictive relationship between mechanical properties of carbon fibers and spectral parameters exists. This shortcoming is due to the use of numerous fitting functions to evaluate Raman spectra of carbon fibers and the inconsistencies in establishing the best fitting models in a statistically robust fashion. To address this gap, we present a comprehensive work on the Raman spectra of carbon fibers that combines a vast library of experimental data with a robust numerical analysis and a statistical evaluation of a wide range of suggested fitting models. This manuscript begins with a brief review of the commonly applied fitting models. Then, the Raman spectra of 32 commercially available polyacrylonitrile-based carbon fibers collected at excitation wavelengths 532, 633, and 785 nm are presented and the best fit for all fibers is evaluated based on several statistical criteria in conjunction with numerical calculations and physical arguments. The results suggest that high-performance fibers must be fit with at least five peaks, whereas high-tensile modulus fibers are best fit with at least six distinct peaks. Finally, we employ simultaneous fitting of the Raman spectra of specific fibers and wavelengths and demonstrate that strong correlations exist between mechanical properties and the D1 peak position and shape across the range of evaluated mechanical properties. We suggest straightforward improvements in fitting analysis procedures that can be implemented to increase coherency in the understanding of the underlying carbon fiber microstructure intuited from Raman spectroscopy.

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References

  1. Newcomb BA (2016) Processing, structure, and properties of carbon fibers. Composites A 91:262

    CAS  Google Scholar 

  2. Böhm R, Thieme M, Wohlfahrt D, Wolz DS, Richter B, Jäger H (2018) Reinforcement systems for carbon concrete composites based on low-cost carbon fibers. Fibers 6:56

    Google Scholar 

  3. Matsumoto T (1985) Mesophase pitch and its carbon fibers. Pure Appl Chem 57:1553–62

    CAS  Google Scholar 

  4. Chernyak SA, Ivanov AS, Maslakov KI, Egorov AV, Shen Z, Savilov SS, Lunin VV (2017) Oxidation, defunctionalization and catalyst life cycle of carbon nanotubes: a Raman spectroscopy view. Phys Chem Chem Phys 19:2276

    CAS  Google Scholar 

  5. Cuesta A, Dhamelincourt P, Laureyns J, Martínez-Alonso A, Tascón JMD (1994) Raman microprobe studies on carbon materials. Carbon 32:1523–32

    CAS  Google Scholar 

  6. Sadezky A, Muckenhuber H, Grothe H, Niessner R, öschl U. Raman microspectroscopy of soot and related carbonaceous materials: spectral analysis and structural information

  7. Chabalala VP, Wagner N, Potgieter-Vermaak S (2011) Investigation into the evolution of char structure using Raman spectroscopy in conjunction with coal petrography; Part 1. Fuel Process Technol 92:750–6

    CAS  Google Scholar 

  8. Sze S-K, Siddique N, Sloan JJ, Escribano R (2001) Raman spectroscopic characterization of carbonaceous aerosols. Atmos Environ 35:561–8

    CAS  Google Scholar 

  9. Bonal L, Quirico E, Bourot-Denise M, Montagnac G (2006) Determination of the petrologic type of CV3 chondrites by Raman spectroscopy of included organic matter. Geochim Cosmochim Acta 70:1849–63

    CAS  Google Scholar 

  10. Bonal L, Bourot-Denise M, Quirico E, Montagnac G, Lewin E (2007) Organic matter and metamorphic history of CO chondrites. Geochim Cosmochim Acta 71:1605–23

    CAS  Google Scholar 

  11. Coccato A, Jehlicka J, Moens L, Vandenabeele P (2015) Raman spectroscopy for the investigation of carbon-based black pigments. J Raman Spectrosc 46:1003–15

    CAS  Google Scholar 

  12. Goler S, Yardley JT, Cacciola A, Hagadorn A, Ratzan D, Bagnall R (2016) Characterizing the age of ancient Egyptian manuscripts through micro-Raman spectroscopy. J Raman Spectrosc 47:1185–93

    CAS  Google Scholar 

  13. Goler S, Hagadorn A, Ratzan DM, Bagnall R, Cacciola A, McInerney J, Yardley JT (2019) Using Raman spectroscopy to estimate the dates of carbon-based inks from Ancient Egypt. J Cult Herit 38:106–17

    Google Scholar 

  14. Daly NS, Sullivan M, Lee L, Trentelman K (2018) Multivariate analysis of Raman spectra of carbonaceous black drawing media for the in situ identification of historic artist materials. J Raman Spectrosc 49:1497–1506

    CAS  Google Scholar 

  15. Deldicque D, Rouzaud J-N (2020) Temperatures reached by the roof structure of Notre-Dame de Paris in the first of April 15th 2019 determined by Raman paleothermometry. Comptes Rendus Géoscience 352:7–18

    Google Scholar 

  16. Huang Y, Young RJ (1994) Microstructure and mechanical properties of pitch-based carbon fibres. J Mater Sci 29:4027–36. https://doi.org/10.1007/BF00355965

    Article  CAS  Google Scholar 

  17. Huang Y, Young RJ (1995) Effect of fibre microstructure upon the modulus of PAN- and pitch-based carbon fibres. Carbon 33:97–107

    CAS  Google Scholar 

  18. Liu F, Wang H, Xue L, Fan L, Zhu Z (2008) Effect of microstructure on the mechanical properties of PAN-based carbon fibers during high-temperature graphitization. J Mater Sci 43:4316–22. https://doi.org/10.1007/s10853-008-2633-y

    Article  CAS  Google Scholar 

  19. Melanitis N, Tetlow PL, Galiotis C, Smith SB (1994) Compressional behaviour of carbon fibres. J Mater Sci 29:786–99. https://doi.org/10.1007/BF00445995

    Article  CAS  Google Scholar 

  20. Wang M-L, Bian W-F (2020) The relationship between the mechanical properties and microstructures of carbon fibers. New Carbon Mater 35:42–9

    CAS  Google Scholar 

  21. Frank O, Tsoukleri G, Riaz I, Papagelis K, Parthenios J, Ferrari AC, Geim AK, Novoselov KS, Galiotis C (2011) Development of a universal stress sensor for graphene and carbon fibres. Nat Commun 2:255

    Google Scholar 

  22. Lu J, Li W, Kang H, Feng L, Xu J, Liu R (2020) Microstructure and properties of polyacrylonitrile based carbon fibers. Polym Test 81:106267

    CAS  Google Scholar 

  23. Qian X, Wang X, Zhong J, Zhi J, Heng F, Zhang Y, Song S (2019) Effect of fiber microstructure studied by Raman spectroscopy upon the mechanical properties of carbon fibers. J Raman Spectrosc 50:665–73

    CAS  Google Scholar 

  24. Cançado LG, Jorio A, Pimenta MA (2007) Measuring the absolute Raman cross section of nanographites as a function of laser energy and crystallite size. Phys Rev B 76:064304

    Google Scholar 

  25. Couzi M, Bruneel J-L, Talaga D, Bokobza L (2016) A multi wavelength Raman scattering study of defective graphitic carbon materials: the first order Raman spectra revisited. Carbon 107:388–94

    CAS  Google Scholar 

  26. Ferrari AC, Robertson J (2000) Interpretation of Raman spectra of disordered and amorphous carbon. Phys Rev B 61:14095

    CAS  Google Scholar 

  27. Ferrari AC, Robertson J (2001) Resonant Raman spectroscopy of disordered, amorphous, and diamondlike carbon. Phys Rev B 64:075414

    Google Scholar 

  28. Cancado LG, Jorio A, Martins Ferreira EH, Stavale F, Achete CA, Capaz RB, Moutinho MVO, Lombardo A, Kulmala TS, Ferrari AC (2011) Quantifying defects in graphene via Raman spectroscopy at different excitation energies. Nano Lett 11:3190–96

    CAS  Google Scholar 

  29. Kaburagi Y, Yoshida A, Hishiyama Y (2016) Raman spectroscopy. Mater Sci Eng Carbon 125–152

  30. Zickler GA, Smarsly B, Gierlinger N, Peterlik H, Paris O (2006) A reconsideration of the relationship between the crystallite size \(\text{ L}_a\) of carbons determined by X-ray diffraction and Raman spectroscopy. Carbon 44:3239–3246

    CAS  Google Scholar 

  31. Tuinstra F, Koenig JL (1970) Characterization of graphite fiber surfaces with Raman spectroscopy. J Compos Mater 4:492–499

    CAS  Google Scholar 

  32. Cançado LG, Takai K, Enoki T, Endo M, Kim YA, Mizusaki H, Jorio A, Coelho LN, Magalhães-Paniago R, Pimenta MA (2006) General equation for the determination of the crystallite size \(\text{ L}_a\) of nanographite by Raman spectroscopy. Appl Phys Lett 88:163106

    Google Scholar 

  33. Matthews MJ, Pimenta MA, Dresselhaus G, Dresselhaus MS, Endo M (1999) Origin of dispersive effects of the Raman D band in carbon materials. Phys Rev B 59:R6585(R)

    Google Scholar 

  34. Mallet-Ladeira P, Puech P, Toulouse C, Cazayous M, Ratel-Ramond N, Weisbecker P, Vignoles GL, Monthioux M (2014) A Raman study to obtain crystallite size of carbon materials: A better alternative to the Tuinstra–Koenig law. Carbon 80:629–639

    CAS  Google Scholar 

  35. Knight DS, White WB (1989) Characterization of diamond films by Raman spectroscopy. J Mater Res 4:385–393

    CAS  Google Scholar 

  36. Cuesta A, Dhamelincourt P, Laureyns J, Martínez-Alonso A, Tascón JMD (1998) Comparative performance of X-ray diffraction and Raman microprobe techniques for the study of carbon materials. J Mater Chem 8:2875–2879

    CAS  Google Scholar 

  37. Maslova OA, Ammar MR, Guimbretière G, Rouzaud J-N, Simon P (2012) Determination of crystallite size in polished graphitized carbon by Raman spectroscopy. Phys Rev B 86:134205

    Google Scholar 

  38. Okuda H, Young RJ, Wolverson D, Tanaka F, Yamamoto G, Okabe T (2018) Investigating nanostructures in carbon fibres using Raman spectroscopy. Carbon 130:178–184

    CAS  Google Scholar 

  39. Nikiel L, Jagodzinski PW (1993) Raman spectroscopic characterization of graphites: a re-evaluation of spectra/structure correlation. Carbon 31:1313–1317

    CAS  Google Scholar 

  40. Galiotis C, Batchelder DN (1988) Strain dependences of the first- and second-order Raman spectra of carbon fibres. J Mat Sci Lett 7:545–7

    Google Scholar 

  41. Kobayashi T, Sumiya K, Fukuba Y, Fujie M, Takahagi T, Tashiro K (2011) Structural heterogeneity and stress distribution in carbon fiber monofilament as revealed by synchrotron micro-beam X-ray scattering and micro-Raman spectral measurements. Carbon 49:1646–52

    CAS  Google Scholar 

  42. Okuda H, Young RJ, Tanaka F, Wantanabe J, Okabe T (2016) Tensile failure phenomena in carbon fibres. Carbon 107:474–81

    CAS  Google Scholar 

  43. Robinson IM, Zakikani M, Day RJ, Young RJ, Galiotis C (1987) Strain dependence of the Raman frequencies for different types of carbon fibres. J Mater Sci Lett 6:1212–4

    CAS  Google Scholar 

  44. Sakata H, Dresselhaus G, Dresselhaus MS, Endo M (1988) Effect of uniaxial stress on the Raman spectra of graphite fibers. J Apply Phys 63:2769

    CAS  Google Scholar 

  45. Tanaka F, Okabe T, Okuda H, Kinloch IA, Young RJ (2013) The effect of nanostructure upon the compressive strength of carbon fibres. J Mater Sci 48:2104–10. https://doi.org/10.1007/s10853-012-6984-z

    Article  CAS  Google Scholar 

  46. Washer G, Blum F Jr (2008) Raman Spectroscopy for the Nondestructive Testing of Carbon Fiber. Res Lett Mater Sci 2008:693207

    Google Scholar 

  47. Lévêque D, Auvray M-H (1996) Study of carbon-fibre strain in model composites by Raman spectroscopy. Compos Sci Technol 56:749–54

    Google Scholar 

  48. Mohiuddin TMG, Lombardo A, Nair RR, Bonetti A, Savini G, Jalil R, Bonini N, Basko DM, Galiotis C, Marzari N, Novoselov KS, Geim AK, Ferrari AC (2009) Uniaxial strain in graphene by Raman spectroscopy: G peak splitting, Grüneisen parameters, and sample orientation. Phys Rev B 79:205433

    Google Scholar 

  49. Beyssac O, Rouzaud J-N, Goffé B, Brunet F, Chopin C (2002) Graphitization in a high-pressure, low-temperature metamorphic gradient: a Raman microspectroscopy and HRTEM study. Contrib Mineral Petrol 143:19–31

    CAS  Google Scholar 

  50. Larouche N, Stansfield BL (2010) Classifying nanostructured carbons using graphitic indices derived from Raman spectra. Carbon 48:620–9

    CAS  Google Scholar 

  51. Li X, Hayashi J-I, Li C-Z (2006) Volatilisation and catalytic effects of alkali and alkaline earth metallic species during the pyrolysis and gasification of Victorian coal. Part VII. Raman spectroscopic study on the changes in char structure during the catalytic gasification in air. Fuel 85:1509–17

    CAS  Google Scholar 

  52. Meškinis S, Gudaitis R, Vasiliauska A, Tamulevičius S, Niaura G (2020) Multiwavelength raman scattering spectroscopy study of graphene synthesized on Si(100) and \(\text{ SiO}_2\) by microwave plasma-enhanced chemical vapor deposition. Phys Status Solidi RRL 14:1900462

    Google Scholar 

  53. Vautard F, Ozcan S, Paulauskas F, Spruiell JE, Meyer H, Lance MJ (2012) Influence of the carbon fiber surface microstructure on the surface chemistry generated by a thermo-chemical surface treatment. Appl Surf Sci 261:473–80

    CAS  Google Scholar 

  54. Cai JY, McDonnell J, Brackley C, O’Brien L, Church JS, Millington K, Smith S, Phair-Sorenson N (2016) Polyacrylonitrile-based precursors and carbon fibers derived from advanced RAFT technology and conventional methods - The 1st comparative study. Mater Today Commun 9:22–9

    CAS  Google Scholar 

  55. Vautard F, Dentzer J, Nardin M, Schultz J, Defoort B (2014) Influence of surface defects on the tensile strength of carbon fibers. Appl Surf Sci 332:185–93

    Google Scholar 

  56. Ager JW III, Veirs DK, Shamir J, Rosenblatt GM (1990) Laser heating effects in the characterization of carbon fibers by Raman spectroscopy. J Appl Phys 68:3598

    CAS  Google Scholar 

  57. Gao A, Su C, Luo S, Tong Y, Xu L (2011) Densification mechanism of polyacrylonitrile-based carbon fiber during heat treatment. J Phys Chem Sol 72:1159–64

    CAS  Google Scholar 

  58. Hagberg J, Leijonmarck S, Lindbergh G (2016) High precision coulometry of commercial PAN-based carbon fibers as electrodes in structural batteries. J Electrochem Soc 163:A1790–7

    CAS  Google Scholar 

  59. Hu JL, Huang JH, Chih YK, Chuang CC, Chen JP, Cheng SH, Horng JL (2009) Effects of thermal treatments on the supercapacitive performances of PAN-based carbon fiber electrodes. Diam Relat Mater 18:511–5

    CAS  Google Scholar 

  60. Li D, Wang H, Wang X (2007) Effect of microstructure on the modulus of PAN-based carbon fibers during high temperature treatment and hot stretching graphitization. J Mater Sci 42:4642–9. https://doi.org/10.1007/s10853-006-0519-4

    Article  CAS  Google Scholar 

  61. Li Z, Wang J, Tong Y, Xiao S, Xu L (2013) Microstructural evolution during oxidative ablation in air for polyacrylonitrile based carbon fibers with different graphite degrees. Surf Interface Anal 45:787–92

    CAS  Google Scholar 

  62. Li B, Feng Y, Qian G, Zhang J, Zhuang Z, Wang X (2013) The effect of gamma ray irradiation on PAN-based intermediate modulus carbon fibers. J Nucl Mat 443:26–31

    CAS  Google Scholar 

  63. Li D, Lu C, Wu G, Yang Y, Feng Z, Li X, An F, Zhang B (2014) Heat-induced internal strain relaxation and its effect on the microstructure of polyacrylonitrile-based carbon fiber. J Mater Sci Technol 30:1051–8

    CAS  Google Scholar 

  64. Wang H, Wang Y, Li T, Wu S, Xu L (2014) Gradient distribution of radial structure of PAN-based carbon fiber treated by high temperature. Prog Nat Sci Mat Int 24:31–4

    Google Scholar 

  65. Chieu TC, Dresselhaus MS, Endo M (1982) Raman studies of benzene-derived graphite fibers. Phys Rev B 26:5867

    CAS  Google Scholar 

  66. Gutmann P, Moosburger-Will J, Kurt S, Xu Y, Horn S (2019) Carbonization of polyacrylonitrile-based fibers under defined tensile load: influence on shrinkage behavior, microstructure, and mechanical properties. Polym Degrad Stab 163:174–184

    CAS  Google Scholar 

  67. Endo M, Kim C, Karaki T, Tamaki T, Nishimura Y, Matthews MJ, Brown SDM, Dresselhaus MS (1998) Structural analysis of the B-doped mesophase pitch-based graphite fibers by Raman spectroscopy. Phys Rev B 58:8991

    CAS  Google Scholar 

  68. Steudle LM, Frank E, Ota A, Hageroth U, Henzler S, Schuler W, Neupert R, Buchmeiser MR (2017) Carbon fibers prepared from melt spun peracylated softwood lignin: an integrated approach. Macromol Mater Eng 302:1600441

    Google Scholar 

  69. Tibbetts GG, Doll GL, Gorkiewicz DW, Moleski JJ, Perry TA, Dasch CJ, Balogh MJ (1993) Physical properties of vapor-grown carbon fibers. Carbon 31:1039–47

    CAS  Google Scholar 

  70. Mallet-Ladeira P, Puech P, Weisbecker P, Vignoles GL, Monthioux M (2014) Behavior of Raman D band for pyrocarbons with crystallite size in the 2–5 nm range. Appl Phys A 114:759–763

    CAS  Google Scholar 

  71. Li D, Lu C, Wu G, Yang Y, An F, Feng Z, Li X (2014) Structural heterogeneity and its influence on the tensile fracture of PAN-based carbon fibers. RSC Adv 4:60648

    CAS  Google Scholar 

  72. Melanitis N, Tetlow PL, Galiotis C (1996) Characterization of PAN-based carbon fibres with laser Raman spectroscopy. J Mater Sci 31:851–60. https://doi.org/10.1007/BF00352882

    Article  CAS  Google Scholar 

  73. Hao X, Yonggen L, Mouhua W, Xianying Q, Weizhe Z, Jian L (2013) Effect of gamma-irradiation on the mechanical properties of polyacrylonitrile-based carbon fiber. Carbon 52:427–39

    Google Scholar 

  74. Niu Q, Zhao S, Gao K, Wang L (2019) Polyacrylonitrile-based nitrogen-doped carbon materials with different micro-morphology prepared by electrostatic field for supercapacitors. J Electron Mater 48:5264–72

    CAS  Google Scholar 

  75. Vázquez-Santos MB, Geissler E, László K, Rouzaud J-N, Martínez-Alonso A, Tascón JMD (2012) Comparative XRD, Raman, and TEM study on graphitization of PBO-derived carbon fibers. J Phys Chem C 116:257–68

    Google Scholar 

  76. Langner J, Bruns M, Dixon D, Nefedov A, Wöll Ch, Scheiba F, Ehrenberg H, Roth C, Melke J (2016) Surface properties and graphitization of polyacrylonitrile based fiber electrodes affecting the negative half-cell reaction in vanadium redox flow batteries. J Power Sources 321:210–8

    CAS  Google Scholar 

  77. Yao L, Yang W, Li S, Sha Y, Tan J, An Y, Li H (2017) Graphitization of PAN-based carbon fibers by \(\text{ CO}_2\) laser irradiation. Carbon Lett 24:97–102

    Google Scholar 

  78. Zhu Y, Sun S, Xu Y, Zhao C, Hu C, Cheng J, Zhao X (2020) Preparation and characterization of pitch coke from oxidized polymerized pitch. Asia-Pac J Chem Eng e2497

  79. Ting Z, Lehua Q, Shaolin L, Xujiang C, Wenlong T, Jiming Z (2019) Evaluation of the effect of PyC coating thickness on the mechanical properties of T700 carbon fiber tows. Appl Surf Sci 463:310–21

    Google Scholar 

  80. Brown SDM, Jorio A, Corio P, Dresselhaus MS, Dresselhaus G, Saito R, Kneipp K. Origin of the Breit–Wigner–Fano lineshape of the tangential G-band feature of metallic carbon nanotubes. Phys Rev B 63:155414

  81. Cançado LG, Pimenta MA, Neves BRA, Dantas MSS, Jorio A (2004) Influence of the atomic structure on the Raman spectra of graphite edges. Phys Rev Lett 93:247401

    Google Scholar 

  82. Sui X, Xu Z, Hu C, Chen L, Liu L, Kuang L, Ma M, Zhao L, Li J, Deng H (2016) Microstructure evolution in \(\gamma\)-irradiated carbon fibers revealed by a hierarchical model and Raman spectra from fiber section. Compos Sci Technol 130:46–52

    CAS  Google Scholar 

  83. Zhou G, Liu Y, He L, Guo Q, Ye H (2011) Microstructure difference between core and skin of T700 carbon fibers in heat-treated carbon/carbon composites. Carbon 49:2883–2892

    CAS  Google Scholar 

  84. Ishida H, Fukuda H, Katagiri G, Ishitani A (1986) An application of surface-enhanced Raman scattering to the surface characterization of carbon materials. Appl Spectrosc 40:322–30

    CAS  Google Scholar 

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Acknowledgements

The authors thank A. Miskowiec, R. Archibald, A. Belianinov, and E. Kirby for critical review of the manuscript.

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Correspondence to Z. E. Brubaker.

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Appendix

Appendix

Figure 14 shows example spectra of all measured fibers at each of the measured excitation wavelengths. Only subtle changes are observed across all SM and IM fibers, although HM fibers show much sharper peaks, and the D2 peak is visually obvious.

Figure 14
figure 14

Example spectra collected with a 532 nm, b 633 nm, and c 785 nm excitation wavelengths for all measured fibers in order of increasing TM listed in Table 2. Uncertainties are smaller than the markers for all spectra and wavelengths

Figure 15 shows the fit components for all models applied to a single Raman spectrum of IM7-GP. As discussed in the main text, significant structure remains in the residual up to four peaks. The fit components demonstrate that the peak amplitudes, positions, and widths strongly depend on the selected fitting model.

Figure 15
figure 15

Example fits (black lines), residuals (offset blue line), and fit components (dashed gray lines) for all fitting models applied to a single Raman spectrum of IM7-GP collected at 532 nm

Figures 16 and 17 show the inverse-variance weighted averaged spectral parameters as a function of TM for each fiber for 4P_1a and 5P_1a fitting applied to SM and IM fibers and 6P_1a fitting applied to HM fibers. Most obtained spectral parameters are similar to those obtained via simultaneous fitting. These parameter values were used to generate numerical datasets, as discussed in the main text.

Figure 16
figure 16

Spectral parameters for 4P_1a obtained from an inverse-variance weighted average of the measurements performed for each fiber type, wavelength, sizing, and tow. Uncertainties correspond to the standard deviation of the weighted mean, \(\sigma =(\sum _i\sigma _i^{-2})^{-2}\). As described in the text, the D3 and D4 peaks were fit with Gaussian line shapes

Figure 17
figure 17

Spectral parameters for 5P_1a obtained from an inverse-variance weighted average of the measurements performed for each fiber type, wavelength, sizing, and tow. Uncertainties correspond to the standard deviation of the weighted mean, \(\sigma =(\sum _i\sigma _i^{-2})^{-2}\). As described in the text, the D3 and D4 peaks were fit with Gaussian line shapes

Figure 18 shows the averaged spectral parameters obtained from the numerical calculations. For data generated from 4P_1a parameters and fit with 4P_1a, D1 and G peak parameters are generally reliable, although n\(_G\) and n\(_{D1}\) show significant (10–20%) uncertainties. For the D3 and D4 peaks, the positions show significant uncertainties in the range of 5 to 20 \(\hbox {cm}^{-1}\), up to about 10% variations in peak widths, and large uncertainties in \(\hbox {I}_{{D4}}\), although \(\hbox {I}_{{D3}}\) is generally reliable. As expected, applying a 5P fitting model to the 4P_1a generated data yields poor values for most spectral parameters, although the spectral parameters of the D1 peak are generally reliable, even if this fitting model is chosen.

Figure 18
figure 18

All averaged calculated spectral parameters plotted against the values used to generate the spectra. The values used to generate the spectra correspond to the averaged values of 4P_1a fits to the experimental data, and the color shades correspond to the wavelength of the fit experimental data. Colors and markers correspond to the applied fit to the generated data. Error bars correspond to the standard deviation of the 1000 fits to each set of generating parameters. Solid red lines correspond to \(y=x\); deviations from this line indicate a difference between fit and generated values

Figure 19 shows the fit parameters obtained from 5P_1a fitting applied to 5P_1a generated data in which the intensity was increased by one order of magnitude. Here, the uncertainties are much smaller than for the original, non-scaled data, though the data collected at 785 nm still shows prohibitively large uncertainties for many spectral parameters.

Figure 19
figure 19

Averaged fit parameters plotted against the generating parameters. The values used to generate the spectra correspond to the averaged values of 5P_1a fits to the experimental spectra. Here, the intensity of the simulated data was increased by one order of magnitude. The color shades correspond to the wavelength at which the generating parameters were extracted. Colors and markers correspond to the applied fit to the generated data. Error bars correspond to the standard deviation of the 1000 fits to each set of generating parameters. Solid red lines correspond to \(y= x\); deviations from this line indicate difference between fit and generated values

Figure 20 shows the fit components of all fits applied to a spectrum of the HM63-GP fiber at 532 nm. Here, the residual shows some structure, even at 8P fits, although it is generally centered near peaks included in the fitting. This might suggest that alternate peak shapes should be considered.

Figure 20
figure 20

Example fits (black lines), residuals (offset blue line), and fit components (dashed gray and black lines) for all fitting models applied to a single Raman spectrum of HM63-GP collected at 532 nm. The dashed black lines correspond to the common five peaks of all fitting models, whereas the dashed gray lines correspond to the additional peaks and are scaled by a factor of 2 for visibility

Figure 21 shows the fit frequencies of HM fibers for all specific fibers measured. As observed for SM and IM fibers, several models are recommended for the 10 fibers measured of a given fiber type.

Figure 21
figure 21

Fit model selection based on \(\chi _{\mathrm{red}}^2\), AIC, and BIC of all measured HM fibers

Figure 22 shows the spectral parameters obtained from 5P_1a fitting of SM and IM fibers and 6P_1a fitting of HM fibers as a function of TS. No significant correlations are observed.

Figure 22
figure 22

Spectral parameters from simultaneous fitting obtained from 5P_1a fitting of SM and IM fibers and 6P_1a fitting of HM fibers as a function of TS. The uncertainties are significantly lower than those observed in the single spectral fitting. Solid lines correspond to linear fits discussed in the text. Marker sizes correspond to the number of spectra simultaneously fit. No significant correlations are observed.

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Brubaker, Z.E., Langford, J.J., Kapsimalis, R.J. et al. Quantitative analysis of Raman spectral parameters for carbon fibers: practical considerations and connection to mechanical properties. J Mater Sci 56, 15087–15121 (2021). https://doi.org/10.1007/s10853-021-06225-1

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