**2. Principle and instrumentation**

#### **2.1. Raman spectroscopy**

The Raman effect is due to inelastic interaction between photons and atomic bonds. In this process, the scattered photons lose or gain energy with respect to the incident photons by vibrating or stabilising the atomic bonds of the sample. This effect leads to a shift in energy called the Stokes shift if the photons lose energy and the Anti-Stokes shift if the photons gain energy. At room conditions, the Stokes part of the Raman signal is generally stronger and is, therefore, generally used in Raman analysis. Due to the quantification of the energy and to the activated vibrational modes, photons are only scattered for particular energies and thus for particular wavelengths. Therefore, Raman scattering of a monochromatic light by molecular entities or an ordered solid will give spectra consisting of sharp spectral lines. Most systems today use a CCD camera interfaced with the spectrometer. The collected signal is then represented in a graph showing the number of photons versus wavenumber, i.e., the shift in cm−1 with respect to the incident beam, the laser wavelength corresponding then to 0 cm−1. The spectral resolution is limited by the CCD camera resolution and by the grating used to diffract the light. It also depends on the laser wavelength. Since the Raman effect is sensitive to atomic bonds, a Raman spectrum is associated with only one compound and its intensity is proportional to its concentration. Polymorphic minerals (similar compositions but different crystalline structures) will thus have different spectra. For example, anatase, rutile and brookite have different Raman spectra despite their similar composition (TiO2). It is important to note that different parameters may influence the Raman signal, such as instrumental setup, structural defects, traces elements, internal stresses or temperature [1–3] (**Figure 1**). Although these parameters may sometimes complicate interpretation, some of them can also be used to measure particular properties, for example, the shift related to internal stresses [4].

Finally, the Raman effect is relatively complex to model, and the identification of a compound is generally made by comparison with reference spectra found in the literature or in databases. More information about the Raman effect can be found in this book or others [5–7].

**Figure 1.** Origins of the parameters and modifications of the Raman spectrum [1].

#### **2.2. Instrumentation**

on sample transparency. For technical reasons, the technique began to be widely used only at the beginning of the 1980s with the generalisation of lasers. At the end of the 1990s, Raman spectroscopy underwent a second phase of development with the introduction of Charge Couple Device (CCD) technology, which has widely improved the sensitivity of spectrometers. These technical revolutions allow acquisition of a Raman spectrum in only few milliseconds. This strong decrease in the acquisition time permitted development of new applications, in particular Raman mapping. This technique consists of scanning the sample with the laser while acquiring

Here, we present the principle of the technique and the basis of the associated data processing followed by an overview of the information that can be extracted from Raman mapping to improve mineralogical and petrological analyses. In particular, we discuss how it can be used to study the general composition of rocks, to detect and identify small phases, or to differentiate minerals whose spectra are very close. More exotic uses of the collected signal are also presented, e.g., detection of particular phases using luminescence. Finally, we illustrate the

The Raman effect is due to inelastic interaction between photons and atomic bonds. In this process, the scattered photons lose or gain energy with respect to the incident photons by vibrating or stabilising the atomic bonds of the sample. This effect leads to a shift in energy called the Stokes shift if the photons lose energy and the Anti-Stokes shift if the photons gain energy. At room conditions, the Stokes part of the Raman signal is generally stronger and is, therefore, generally used in Raman analysis. Due to the quantification of the energy and to the activated vibrational modes, photons are only scattered for particular energies and thus for particular wavelengths. Therefore, Raman scattering of a monochromatic light by molecular entities or an ordered solid will give spectra consisting of sharp spectral lines. Most systems today use a CCD camera interfaced with the spectrometer. The collected signal is then represented in a graph showing the number of photons versus wavenumber, i.e., the shift in cm−1 with respect to the incident beam, the laser wavelength corresponding then to 0 cm−1. The spectral resolution is limited by the CCD camera resolution and by the grating used to diffract the light. It also depends on the laser wavelength. Since the Raman effect is sensitive to atomic bonds, a Raman spectrum is associated with only one compound and its intensity is proportional to its concentration. Polymorphic minerals (similar compositions but different crystalline structures) will thus have different spectra. For example, anatase, rutile and brookite have different Raman spectra despite their similar composition (TiO2). It is important to note that different parameters may influence the Raman signal, such as instrumental setup, structural defects, traces elements, internal stresses or temperature [1–3] (**Figure 1**). Although these parameters may sometimes complicate interpretation, some of them can also be used to

measure particular properties, for example, the shift related to internal stresses [4].

spectra so that spatial distribution can be added to structural information.

discussion using a number of different types of rocks and minerals.

**2. Principle and instrumentation**

**2.1. Raman spectroscopy**

164 Raman Spectroscopy and Applications

Raman mapping consists of scanning a sample with the laser beam while acquiring spectra. For the study example, we present here, a WITec Alpha500 RA Raman spectrometer was used. Other systems from Renishaw, Horiba Jobin Yvon, Thermo Fisher or Bruker, for example, may use slightly different methods for mapping, but the general principle of scanning remains the same. The general discussion of this chapter can thus be applied to any other system.

This study was made using a CW green Nd:YAG frequency doubled laser with a wavelength of λ = 532 nm. The laser beam is focused on the sample using optical microscope objectives and optical observations of the analysed area are made with a camera. The spectral resolution of the spectrometer is of 1 and 3 cm−1 using 1800 and 600 g/mm gratings, respectively. Surface scanning is made by moving the sample below the objective along successive lines using motorised and/or piezoelectric scan tables. The instrument used is equipped with two positioning systems: (1) a small-scale system working with piezoelectric ceramics that can analyse an area of 200 × 200 μm in the horizontal plan and 20 μm in the vertical direction and (2) a large-scale motorised system that can move the sample over a distance of 15 × 10 cm horizontally and 2 cm vertically.

Raman mapping systems are generally confocal, i.e. only the signal coming from the near object focal plane is redirected to the spectrometer. This is done by placing a pin hole in the image focal plane of the microscope. The volume used for the analysis is then reduced and the inplane resolution is slightly increased, depending on the size of the pin hole, the objective and the laser wavelength. The main interest of the confocality is to permit 3D imaging using a stacking process by acquiring Raman maps at different depths. It is important to note that the depth of analysis depends on the refractive index of the material; there is a difference between the apparent depth, corresponding to the distance with respect to the sample surface, and the true depth of analysis (**Figure 2**).

**Figure 2.** Apparent depth *D*0 versus true depth *Di* of analysis in optical microscopy when analysing (a) a material with a refractive index equal to *n*1, (b) a material with a refractive index equal to *n*2 with *n*2 > *n*1 and (c) when analysing across *n* different materials of refractive index *ni* and thickness *ei* .

The ratio between the true depth *Di* and the apparent depth *D*0 is given by the following equation:

$$\frac{D\_l}{D\_0} = \frac{\tan i\_0}{\tan i\_l} \tag{1}$$

where *i*0 and *i*1 are the maximal angle with respect to the optical axis in the observation medium (e.g. air, water or oil) and in the analysed material, respectively (see **Figure 2a**). The famous Snell-Descartes law and the definition of the numerical aperture NA give:

$$NA = n\_0.\sin i\_0 = n\_l.\sin i\_l \tag{2}$$

where *n*0 and *ni* are the refractive index of the observation medium and of the analysed material, respectively. Using Eq. (2), and noting that:

$$\tan\left(\arcsin x\right) = \frac{x}{\sqrt{1-x^2}}\tag{3}$$

Eq. (1) finally writes:

$$\frac{D\_l}{D\_0} = \sqrt{\frac{n\_l^2 - NA^2}{n\_0^2 - NA^2}}\tag{4}$$

This ratio is thus all the more important when the difference in refractive index is high (see **Figure 2b**). For example, when analysing quartz (*n*qz = 1.55) in air (*n*air = 1) with an objective having a numerical aperture of *NA* = 0.9, the true depth of analysis is ~2.9 times deeper than the apparent depth corresponding to the mechanical vertical displacement.

In the case where several phases are crossed by the laser (see **Figure 2c**), Eq. (4) can be generalised into:

$$\frac{D\_n}{D\_0} = \sum\_{l=1}^n e\_l \sqrt{\frac{n\_l^2 - NA^2}{n\_0^2 - NA^2}}\tag{5}$$

where *ei* is the thickness of the phase *i*. For 2D maps, the depth of the measurement and the volume analysed are thus different for each phase, and for 3D Raman maps, the volume and the depth of the different phases are associated with different scales in the raw data.

#### **2.3. Raman mapping**

depth of analysis depends on the refractive index of the material; there is a difference between the apparent depth, corresponding to the distance with respect to the sample surface, and the

a refractive index equal to *n*1, (b) a material with a refractive index equal to *n*2 with *n*2 > *n*1 and (c) when analysing

0

where *i*0 and *i*1 are the maximal angle with respect to the optical axis in the observation medium (e.g. air, water or oil) and in the analysed material, respectively (see **Figure 2a**). The famous

.

and thickness *ei*

0 1 tan tan *D i <sup>i</sup>*

( ) <sup>2</sup>

=

1 *<sup>x</sup> <sup>x</sup>*

> 2 2 2 2

0 0 *D n NA i i D n NA* *x*

Snell-Descartes law and the definition of the numerical aperture NA give:

tan arcsin

of analysis in optical microscopy when analysing (a) a material with

and the apparent depth *D*0 is given by the following

*D i* <sup>=</sup> (1)

0 0 .sin .sin *NA n i n i* = = *i i* (2)



are the refractive index of the observation medium and of the analysed material,

true depth of analysis (**Figure 2**).

166 Raman Spectroscopy and Applications

**Figure 2.** Apparent depth *D*0 versus true depth *Di*

across *n* different materials of refractive index *ni*

The ratio between the true depth *Di*

respectively. Using Eq. (2), and noting that:

equation:

where *n*0 and *ni*

Eq. (1) finally writes:

As explained above, Raman mapping consists of scanning the sample with the laser beam while acquiring spectra. The scanned area is then divided into a pixel-assigned array of spectral elements, sometimes called "spexels" [8], as shown in **Figure 3a**.

**Figure 3.** (a) Principles of Raman mapping illustrated using a polished thin section of a metachert from the 3.8 billion years old Isua Greenstone belt, Greenland. The scanned area of the sample is divided into small squares, or spexels, each associated with a Raman spectrum. (b) Raman map of the concentration of quartz in the sample, as identified by the intensity of the main peak at 465 cm−1. (c) Raman map of the composition of the sample obtained by attributing a colour to the main spectral peak of each mineral (yellow for quartz, grey for cumingtonite, pink for apatite and green for graphite). Scan size: 500 × 500 μm2 .

Historically, the first Raman maps were constructed manually by making a map point by point. The sample was then not scanned continuously but was immobile beneath the laser beam during the acquisition of each spectrum (**Figure 4**). These first maps were interesting for the study of homogeneity in materials, but, because of the limited number of spectra associated with this time-consuming method, imaging was not very efficient. With the recent development in fine positioning systems and synchronisation between the positioning system and the CCD detector, automated scanning is now available. This automation allows high resolution mapping point by point as well as by continuous scanning.

**Figure 4.** Principle of Raman mapping. (a) Laser spot size versus area of interest and different ways of scanning, (b) point by point, (c) continuously and horizontally and (d) continuously and vertically. The spectrum associated to each pixel corresponds to the average spectrum of the different associated phases. The concentration map is thus darker where the vermicular structure is analysed. If the spot size is larger than the pixel size (left row), there is oversampling, and the associated maps are the same whatever the method used. However, if the laser spot size is small in comparison with the pixel size (right row), there is undersampling and the associated maps depend on the type of the scan.

In all scanning methods of imaging (e.g. Raman mapping as well as atomic force microscopy, scanning electron microscopy, etc.), the lines are accumulated one by one and the spatial resolution is fixed by the ratio of the width and height of the scanned area over the number of lines and rows, respectively. Then, for a square scan, the time needed to go down a row is very long compared to the time needed to go along a line (for a horizontal scan). The axis parallel to the lines is thus called the fast axis, and the axis perpendicular to the lines is called the slow axis (see **Figure 4**). This notion must be kept in mind while scanning a small area where thermal or mechanical drift may induce deformation in the images (shearing) and/or a loss of focus with the time. During Raman mapping, the spectra are generally accumulated continuously during the scan. The spectrum associated with each point corresponds thus to the average spectrum acquired over a line whose length is fixed by the spatial resolution but whose thickness is equal to the laser spot size. If the spot size is higher than the resolution, the associated map is then under-sampled since not all the area are scanned; a scan obtained over the same area rotated by 90° would give a different result (**Figure 4**). To avoid this effect, the chosen resolution must be at least equal to the spot size. On the other hand, the Rayleigh criterion implies that the resolution cannot be physically higher than half of the spot size as given by the Airy disk equation:

$$S = 1.22 \frac{\lambda}{NA} \tag{6}$$

where *λ* is the laser wavelength, *S* is the laser spot diameter, and *NA* is the numerical aperture of the objective. Using a green laser (*λ* = 532 nm) and the 100× objective (with a numerical aperture of 0.9), the spot size is thus *S* ~ 720 nm in diameter and the maximal physical resolution is thus ~360 nm/pixel. Using a confocal system, this resolution can be slightly decreased by ~10% [6]. However, even if using a higher resolution does not give more information, oversampling could provide a better contrast.

In conclusion, continuous scanning is generally the best choice for imaging due to its rapidity, but point-by-point mapping may be useful when the sample contains fluorescent phases that may drown out the Raman signal of the other phases in the average spectra acquired with the continuous scan method.
