Spectroscopy for Materials Characterization. Группа авторов

1 Radiation–Matter Interaction Principles: Optical Absorption and Emission in the Visible‐Ultraviolet Region

       Simonpietro Agnello

       Department of Physics and Chemistry – Emilio Segrè, University of Palermo, Palermo, Italy

1.1 Empirical Aspects of Radiation–Matter Interaction

      The basic everyday experience of the colors around us inspires the knowledge of the phenomenon of radiation–matter interaction. Sun, the source of daylight, emits a large quantity of electromagnetic field frequencies (ν), or wavelengths (λ). When these rays impinge on matter, they can be reflected (scattered) or absorbed by the constituent atoms and molecules. These phenomena give rise to the appearance of colored objects since the light arriving at our eyes (a light sensor) depends on the emitted radiation or the reflected one, having fewer frequencies than the original sunlight due to the absorption effect of matter around us. In this chapter, some empirical aspects of absorption and emission phenomena will be introduced.

      1.1.1 Optical Absorption: The Lambert–Beer Law

An introductory experiment that highlights the effect of absorption of light is represented in Figure 1.1.

      A parallel beam of lightwave with wavelength λ and intensity I ₀(λ) impinges perpendicularly on a face of a parallelepiped specimen of matter. It is useful to recall that λ and ν are connected by the speed of light c (2.9979 × 10⁸ m⋅s⁻¹ in vacuum): λ = c/ν [1]. Passing through the sample, the light intensity could be reduced, and at the exit, the amount I measured at λ could be diminished to the value I _t(λ) [2–4]. The eventual intensity reduction inside the specimen increases continuously on increasing the size L. If a portion of thickness dx of the sample is considered, it is expected that passing through it, I decreases by a quantity dI (for simplicity, λ will be omitted henceforth). This effect depends on the presence of absorbing centers in the volume considered, on the one side, and on their physical properties, on the other. These features are taken into account by the concentration of centers, N, and by their cross section, σ. Larger is the concentration of centers, larger absorption will take place. On increasing the probability of radiation–matter interaction, σ increases too, as well as the absorption effect. If a homogeneous and isotropic distribution of absorbing centers inside the volume of the sample is considered, it can be assumed that [3]:

(1.1)

where the units are J (cm²⋅s)⁻¹ for I, centers cm⁻³ for N, cm² for σ, and cm for dx. By considering the entire sample, Eq. (1.1) can be integrated to obtain:

      (1.2)

      and determine the solution

(1.3)

In general, from solution (1.3), it is found that at a position x inside the sample

(1.4)

      this is the Lambert–Beer law that expresses the attenuation of light intensity as a function of the thickness of the sample traversed [2, 3]. A typical expected profile of light intensity in traversing a sample is reported in Figure 1.1. It is useful to introduce some quantities commonly associated to the absorption effect. The empirical one is the absorption coefficient defined by the experimental macroscopic measurement of attenuation:

(1.5)

      It is easy to show that α = σN, connecting the macroscopic quantities α and N to the microscopic one σ (see Section 1.2 to find the relation to atomic and molecular properties). Then, we report the instrumental quantity, the optical density (OD), also called absorbance (A) [5, 6]:

(1.6)

      and the transmittance, T:

      (1.7)