Choice of the working conditions for Raman extensometry of carbon and SiC fibers by 2D correlation

Composites Science and Technology 62 (2002) 505–511 www.elsevier.com/locate/compscitech

Choice of the working conditions for Raman extensometry of carbon and SiC fibers by 2D correlation G. Gouadeca, J.-P. Forgerita, Ph. Colombana,b,* a

Laboratoire Dynamique, Interaction et Re´activite´ (LADIR), UMR 7075 (CNRS and Univ. P.&M. Curie), 2 rue H. Dunant, 94320 Thiais, France b De´partement Mate´riaux et Syste`mes Composites (DMSC), ONERA, BP 72, 92322 Chaˆtillon, France Received 17 November 2000; accepted 19 July 2001

Abstract The measurement by Raman extensometry of stresses in fibres used for reinforcing composites requires careful choice of the best suited spectral probe and of working conditions that allow for the best compromise between accuracy and speed. In this paper we show how 2D-correlation methods can be of precious help on both counts, when applied to Raman spectra. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: A. Fibres; A. Ceramics; C. Residual stress; D. Non-destructive testing; D. Raman spectroscopy

1. Introduction The characterisation of heterogeneous materials requires adaptation to the applicable scales. In the case of a fibre-reinforced composite, one must probe the matrix, the preform, materials interfaces (or, possibly, interphases) and even the nano-structure of the fibres (which often contain multiple phases) separately. In this context, Raman micro-spectrometry challenges X-ray micro-beams or EDS, since it analyses the chemistry, the structure and local order of materials, whatever their state, whether amorphous or crystalline. The anharmonicity of bond wells also makes vibrational modes sensitive to stress (and temperature) and Raman micro-spectrometry is becoming a precious tool for mechanical characterisation of composites (Raman extensometry), just as micro-indentation of longer history [1]. Peak shifts remain small however (not exceeding 2.3 cm
1 per GPa for silicon, the basic material in micro-electronic devices when stressed in the (100) direction [2]). Hence the importance of controlling the equipment drift, thermal perturbations from sample heating and the reproducibility of band fitting simulations [2,3]. There are often several possibilities for the latter, especially when

* Corresponding author. Tel.: +33-1-4978-1105; fax: +33-1-49781118. E-mail address: [email protected] (Ph. Colomban).

spectra have multiple, large and overlapping components. Salje and co-workers preferred self-correlation to peak fitting for the treatment of IR spectra recorded as a function of temperature [4]. A definite slope change on the plot of the resulting self-correlation band evidenced a phase transition. This approach has since been used on ceramic fibres Raman spectra [5]. 2D-correlation (C2D) was introduced by Noda [6–8] as a way of studying the correlation between

1 and

2 wavenumbers at different times. We show here how the technique evidences any perturbation influence on spectral parameters and is applicable to any series of perturbed spectra. We shall illustrate this considering either strain ("), wavelength ( l) and incident laser power (P) as the perturbation. Any perturbation p is valid provided each spectrum is identified with an integer n, assigned to it according to increasing p, from 1 to N. C2D will help understand Raman spectra and define optimal experimental conditions to make use of Raman Extensometry on composite materials.

2. Experimental The Raman equipment used to study strained fibres has been described elsewhere [3]. The XY spectrometer (Dilor, France) is coupled with a Innova 70 Ar/Kr laser (Coherent, USA) 12 wavelengths of which were used (458/ 466/473/477/488/497/502/514/531/568/647/676 nm). The

0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(01)00141-5

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G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

light is back-scattered through a microscope (1000), analysed on a CCD detector (2000800) cooled down to liquid nitrogen temperature (Spex/Jobin-Yvon, France). Laser power on the sample is measured with a PD200 photodiode (Ophir, USA). Raman spectra are fitted using a custom-made C2D program (Delphi language; Inprise/Borland, USA). Studied fibres were the highly crystalline FT700 pitch fibre (turbostratic carbon with preferential orientation along the fibre axis) from Tonen (Japan), the Hi-S Nicalon SiC fibre (thread from polycarbosilane, reticulated under electronic irradiation; C/Si(atomic)=1.05) from Nippon Carbon (Japan) and the SCS-6 fibre from Textron (USA). The latter is a composite fibre whose carbon core is covered with CVD SiC.

ð

1 ;

2 Þ ð!Þ and ð

1 ;

2 Þ ð!Þ are calculated via Fourier’s transformation: h i ð þ1 Re I~ 0

i ð!Þ ¼ I

i ðtÞ  cosð!tÞdt t¼
1 h i ð þ1 I

i ðtÞ  sinð!tÞdt ð7Þ Im I~ 0

i ð!Þ ¼ t¼
1

Any excitation can be viewed as a Fourier series— that is to say a sum of harmonic vibrations—and 2Dcorrelations synchronous ð

1 ;

2 Þ and asynchronous ð

1 ;

2 Þ components will be obtained as follows: ð þ1 ð

1 ;

2 Þ ¼ ðð!
1Þ;
2 Þ d!

!¼
1 ð þ1 ð!Þ ð8Þ ð
1 ;
2 Þ ¼ ð
1 ;
2 Þ d! !¼
1

3. Principles of 2D-correlation Noting I

i ðtÞ the spectral intensity, Re[X], Im[X] and X* respectively the real part, the imaginary part and the conjugated of X, the

1 and

2 correlation function is defined by: " # ð T=2 1 Ið

1Þ lim I 

1 ðtÞ  I

2 ð þ tÞ dt ð1Þ cIð
2Þ ð Þ ¼ Re |{z}
2 T !1


T=2

Supposing a harmonic excitation of the system, its response will be similar (with the same pulsation !): I

i ðtÞ ¼ I 0

i ð!Þ  e jð!t
’i Þ ¼ I~ 0

i ð!Þ  e j!t

ð2Þ

where I~ 0
i ð!Þ ¼ I 0
i ð!Þ  e
j’i is the complex amplitude of

the signal: i 1 h ~ 0 ð!Þ  ej! cIIðð


12 ÞÞ ð Þ ¼ Re I~ 0 ð ! Þ  I


1
2
2

ð3Þ

Eq. (3) can be split into in-phase (ð

1 ;

2 Þ ð!Þ) and out of phase ( ð

1 ;

2 Þ ð!Þ) components: cIIðð


12 ÞÞ ð Þ ¼ ð

1 ;

2 Þ ð!Þ  cosð! Þ þ
 sinð! Þ

ð

1 ;

2 Þ ð!Þ

ð4Þ

i h i h i 1 h~0 Re I

1 ð!Þ  Re I~ 0

2 ð!Þ þ Im I~ 0

1 ð!Þ 2h i Im I~ 0

2 ð!Þ ð5Þ

ð

1 ;

2 Þ ð!Þ ¼

i h i h i 1 h~0 Re I

2 ð!Þ  Im I~ 0

1 ð!Þ
Re I~ 0

1 ð!Þ 2h i Im I~ 0

2 ð!Þ ð6Þ

ð

1 ;

2 Þ ð!Þ

¼

Eqs. (1)–(8) present C2Ds general formalism. From a practical point of view, it is n, the variable we defined in our introduction, that will be equivalent to ‘‘time’’. cIIðð


12 ÞÞ
will be a surface in the complex space—a function of N—and the level curves of Fð

1 ;

2 Þ and ð

1 ;

2 Þ will give a bi-dimensional (2D) representation of the correlation. Fourier’s variable will be the ‘‘frequency’’ n/N (!=2 n/N), where n is an integer between 0 and (N
1). Though we defined correlation by a function of N, we must keep in mind that the ‘‘physical parameter’’ it is related to is the [pmin; pmax] interval. ð

1 ;

2 Þ diagonal is nil (anti-symmetric function) whereas any local maximum on ð

;

Þ , called a ‘‘self-peak’’, indicates a band changing due to the perturbation. Extremes away from diagonals (

1 6¼

2 ), also called ‘‘cross peaks’’, provide a chronological information. In the case of ð

1 ;

2 Þ , cross peaks show which intensities are coupled while the perturbation takes place. A positive (negative) sign indicates variations proceeding in the same (opposite) direction. As for ð

1 ;

2 Þ , if ð

1 ;

2 Þ  ð

1 ;

2 Þ is positive, then the signal is perturbed in

1 before

2 (and conversely). Theoretically, C2D should apply to as-recorded spectra. Yet, baseline fluctuations and noise variations generate typical ‘‘streak-like’’ features and a baseline subtraction improves the results. C2D interpretation becomes even simpler if spectra are normalised prior to the calculations [9,10].

4. Results 4.1. C2D signature of spectral fluctuations One advantage of C2D is its great sensitivity [11] but several effects often superimpose on ð

1 ;

2 Þ and ð

1 ;

2 Þ , which makes it difficult to interpret these functions. It is of help to start with elementary situations where only one parameter changes ‘‘as a function of time’’ [9,10,12]. Fig. 1

G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

shows the C2D spectra for two model bands having opposite variations in wavenumber, width or intensity. Intensity fluctuations give more or less circular halos whereas width changes give butterfly wings-like features. As for wavenumber fluctuations, they can easily be recognised by crossing egg timers (of opposite signs) on the synchronous component and 4 zeros on the asynchronous one (crescent-shaped spots). 4.2. Perturbation=excitation wavelength (l): resonant Raman effect Carbon is the most widely used Raman extensometry probe (in NLM and Hi Nicalon grades of Nippon Carbon SiC fibres, the SiC signal is too weak to be of use). Fig. 2 presents Raman spectra recorded with 12 different wavelengths on cross-sections of FT700 (Fig. 2a) and Hi-S (Fig. 2b) fibres. Since the spectrograph’s efficiency changes with l, absolute intensities are useless in comparing the spectra. This is the reason why C2D was calculated (Fig. 2e) after band standardisation (Fig. 2c and d). First order Raman bands of carbonaceous matter are called D, G and D0 [13]. D and G were so named because of their analogy with diamond (1331 cm
1) and graphite (1580 cm
1) signals. As for D0 , it is always observed with D band [14] and their relationship is self evident in Fig. 2c and d. G assignment to the stretching mode of C2sp C2sp aromatic bonds is admitted by many authors (E2g symmetry-band in graphite single crystals). D broadens and moves towards 1340 cm
1 in

507

disordered diamond [15] but we detect it above 1350 cm
1. This underlines a wide dispersion of bond lengths and/or angles and of the electronic shell. D is abnormally large for a ‘‘pure’’ band and a distribution of configurations is likely. The scattering efficiency of diamond being far lower than that of graphite (9.110
7 and 510
5 cm
1/sr, respectively [16]), D band would be weaker if it was only a result of C3sp–C3sp ‘‘diamondlike’’ bonds. D resonant character, particularly obvious with the wavelength-induced shifting (# +50 cm
1/eV [17]) and the 2

D and

D+

G harmonics exaltation under blue excitation [18], proves that this band corresponds to bonds that differ from those of diamond. The main contribution probably comes from intermediate C2sp–C3sp bonds like those encountered in some fullerenes. Indeed, the IG/ID ratio happens to be proportional to the average size L of graphite moieties [19]. IG/ ID is, therefore, equivalent to the ratio of L3 (the density of the C2sp¼C2sp bond responsible for G) divided by L2. Now, the presence of C2sp–C3sp can be expected at the grain boundaries (especially for the Hi–S fibre where carbon is in contact with a sp3 network of SiC), with a L2 density. In conclusion, D might be the contribution of C2sp–C3sp bonds [20]. Moreover, D stands in the region of the bands of non-planar molecules like C70 and carbon nanotubes, where bonds are intermediate between C2sp–C2sp and C3sp–C3sp bonds [21]. The strong resonance under blue excitation is in agreement with our assignment to C3sp
C3sp =2sp mixed bands (we believe the ‘‘purely’’ sp3 contribution is a shoulder we detected on the NLM fibre

Fig. 1. Synchronous () and asynchronous () 2D-correlation components from three independent series of ten ‘‘model’’ two-band spectra (1100 and 1200 cm
1 ; 20 cm
1 widths) with wave numbers (a), widths (b) or intensities (c) varying linearly in opposite ways (increasing for the low wave number band). Overall variations are 10 cm
1 for the shifts, 10% in widths and 50% in intensity.

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G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

Fig. 2. (a) and (b) Spectra recorded with 12 different wavelengths, shown after baseline subtraction; (c) and (d) D and G-based standardisation of Hi–S spectra; (e) 2D-correlation components obtained from the spectra standardised with respect to D (top) or G (bottom) band.

spectrum, when observed with red excitation [5]), since the s!s* and p!p* transitions of graphite absorb in the UV and visible range, respectively. However, other authors attribute D to a so called ‘‘density of state’’ mode of graphite, activated by Brillouin zone folding (a very common phenomenon for anisotropic disorder) and then excited in a selective way by a purely p!p* electronic transition [17].

It is obvious from Fig. 2e that C2D ‘‘signal’’ concentrates around bands that dominate Raman spectra: D band for the Hi-S fibre and G for the FT700. It is the same perturbation which effects are observed in both cases but the signal coming from the less intense bands is systematically concealed. Hence the importance of the spectral zone choice when building C2D figures. C2D derived from D-based standardisation shows only

G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

G intensity changes with l, not its position, nor its width. Besides, D shift proceeds without bandwidth modification. C2D derived from G-based standardisation points out that D shift is coupled with a intensity variation but does not imply bandwidth change. As for D0 , no self-peak is observed but some crossed signal with D and G is obvious. In the former case, signal corresponds to the relative shift of D with respect to D0

509

(a band which is insensitive to l). In latter case, crosscorrelation indicate a fundermental nature difference between G and D0 bands. The wavelength-dependent shift of D might result from an absorption modulation. Comparison of D and D0 in strained fibres might then be useful in order to characterise the mechanical state of ‘‘grain boundaries’’ for different penetration depths.

Fig. 3. (Top) spectra of strained FT700 and Hi–S fibers (l=457.9 nm/P=2 mW); (center) baseline subtraction; (bottom) 2D correlation.

510

G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

Fig. 4. Power influence [1-2-4-6-8-10-15-20 mW] on spectra (l=514.5 nm) and 2D correlation in SCS-6 fiber core.

4.3. Perturbation=fibre strain ("): n=Se (S" < 0) The spectra of fibres under uniaxial tension are given in Fig. 3. There is little effect on the wavenumbers (even when the spectrum preceding the fibre failure is compared with the spectrum ‘‘at rest’’) and its highlighting requires mathematical treatment of the spectra (S" #
9.3 cm
1/% for FT700 fibre but only
3 cm
1/% in SiC fibres [18]). On the other hand, the synchronous C2D function shows characteristic features. First of all, the stress sensitivity of both silicon carbide peaks is weaker (smaller extension) than that of carbon. Regarding asynchronous C2D, only streaks are visible and the noise on the spectra accounts for them. Thus, all bands simultaneously feel the effect of strain, in spite of their assignment to distinct chemical species. Yet, the synchronous signal is dominated by the contribution of G—around 1600 cm
1—in the case of the FT700 fibre while D is of prominent importance in the Hi–S fibre. Of course intensity plays a part in this statement, but it looks as if the macroscopic stress were felt and transmitted by the turbostratic carbon planes of the FT700 fibre, whereas it is dispersed along the grain boundaries in the Hi–S fibre. Besides, the ground level of Hi–S fibre spectra vanishes when strain increases. This can be interpreted as a sign that precipitates reorganise and tend to align in the direction of the solicitation. Any misadjustment of Raman equipment is ruled out since SiC intensity is constant. Moreover, ð

1 ;

2 Þ deformation around 1620 cm
1 suggests D0 has its own sensitivity to traction, which is hard to evidence from mathematical modelling. Lastly, note the 3 last spectra of Hi–S fibre do not show the 675 cm
1 singularity.

4.4. Perturbation=laser power (P) on a SCS-6 fibre Illuminating a sample containing some carbon can induce significant heating and expand the bonds. This results from the strong electronic absorption in the visible range (resonant Raman effect). Fig. 4 shows spectra recorded for different powers on the carbon core of a SCS-6 fibre (l=514.5 nm). The C2D figure is obviously shifted towards the low wavenumber sides as a consequence of a laser-induced heating. The wavenumbers covered by Figs. 3 and 4 are roughly the same. By comparing the two figures, one understands how heating may conceal a stress-induced effect and must definitely be taken into consideration [22]. All in all, chemical species observed through D, G and D0 carbon bands or SiC optic modes seem to have their own behaviour from the mechanical point of view but behave in the same way under the effect of heating. Streaks characteristic of fluctuations (spectral noise) are visible on the asynchronous component but no width change is evidenced. There would therefore not occur any chemical deterioration of carbon, which suggests temperature stays below 400–500 C (oxidation temperature), at least until 20 mW, for the considered wavelength.

5. Conclusion 2D correlation allowed for a better understanding of carbon spectra, which is mandatory if Raman spectroscopy was to be used for stress assessment. The method proved helpful for the choice of the most relevant spectral parameters and for the choice of the best working conditions. It might also be applied to spectra recorded during sample loading to evidence stress transmission.

G. Gouadec et al. / Composites Science and Technology 62 (2002) 505–511

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