Materials Science for Solar Energy Conversion Systems (eBook)

C.G. Granqvist (Herausgeber)

eBook Download: PDF | EPUB

2013 | 1. Auflage
212 Seiten
Elsevier Science (Verlag)
978-1-4832-8757-7 (ISBN)

Infos

Rapid advances in materials technology are creating many novel forms of coatings for energy efficient applications in solar energy. Insulating heat mirrors, selective absorbers, transparent insulation and fluorescent concentrators are already available commercially. Radiative cooling, electrochromic windows and polymeric light pipes hold promise for future development, while chemical and photochemical processes are being considered for energy storage. This book investigates new material advances as well as applications, costs, reliability and industrial production of existing materials. Each contribution represents a landmark in the field of materials science.

Textauszug

Chapter 2

OPTICAL PROPERTIES OF INHOMOGENEOUS TWO-COMPONENT MATERIALS

G.A. Niklasson,     Physics Department, Chalmers University of Technology and University of Gothenburg, S-412 96 Gothenburg, Sweden

ABSTRACT

Effective medium and multiple scattering theories for the optical properties of two-component materials are reviewed. Such materials have numerous applications in the field of coatings for energy efficiency. The transmittance and reflectance of a coating or slab of a composite can be obtained from the effective dielectric and magnetic permeabilities of the material. For materials with inhomogeneities much smaller than the wavelength of the impinging radiation, the effective dielectric permeability can be evaluated in the quasistatic limit. We review the rigorous Bergman-Milton bounds for the effective dielectric permeability as well as various effective medium theories that have been put forward for describing the optical properties of specific microstructures. Specifically we treat the effects of pair and three-point correlations on the bounds and obtain novel effective medium theories taking these effects into account. Materials with large inhomogeneities on the order of, or larger than, the wavelength must be described by different theories. The effective magnetic permeability must be taken into account. The specular reflectance, the direct transmittance and the diffuse scattering are treated by use of a four flux theory.

I INTRODUCTION

An understanding of the optical properties of inhomogeneous materials is very important in the development and optimization of various coatings for energy efficiency. Applications such as solar absorption, radiative cooling and energy efficient windows have prompted a large interest in composite materials. Many coatings used for selective absorption of solar energy are of this class.1 Composites of metal particles in an insulator matrix display a very good selectivity, and have been produced by electrochemical techniques,2–5 electron-beam evaporation6,7 and sputtering.8 Another example of composite selective absorbers are paint coatings9 which consist of an absorbing pigment dispersed in a binder material.

For radiative cooling applications solar reflecting and infrared-transmitting pigmented polymer foils are of interest, as well as ceramics which probably consist of a mixture of an oxide phase and voids.10 As a final example we mention that many visibly transmitting coatings with low emittance – of use for energy-efficient windows – incorporate thin metal films. It has recently been shown that an improved performance can be achieved by inhomogeneous “network” films close to the percolation threshold.11 The aim of this chapter is to review theoretical descriptions of the optical properties of two-component materials. These theories are often very useful in the study of materials for energy-efficient applications. However, this chapter is not a prerequisite for the rest of the book, and the reader mainly interested in technical applications may proceed directly to the topical chapters.

In the development of composite thin films it is of prime importance to establish the connection between the properties of the composite and those of the constituents. This facilitates materials selection and optimization of practical coatings. The optical properties of composite materials can be described in the quasistatic approximation if the size of the inhomogeneities is much smaller than the wavelength of electromagnetic radiation. The optical properties of the material are obtained from the effective dielectric permeability of the composite which can be related to the dielectric permeabilities of the constituents by effective medium theories (EMT’s).12–14 These theories are also sensitively dependent upon the actual microgeometry of the composite material. Actually a rigorous expression for the effective dielectric permeability can only be obtained if the detailed geometrical arrangement (i.e., the n-point correlation functions) of the constituents are known. When limited structural information is available, as is always the case in practice, the various EMT’s can give no more than approximate expressions. However it is possible to obtain rigorous bounds for the effective dielectric permeability.15–18 When more structural information is incorporated into the bounds, they become more narrow. For large size inhomogeneities the quasistatic approximation is not valid and the concept of an effective medium encounters difficulties.19 Scattering becomes important and the optical properties can be described in the framework of radiative transfer and multiple scattering theory.20–22 In the case of very large particles, simplifications are again possible and geometric optics can be used.

In this chapter the various theories that have been put forward to describe the optical properties of composite materials are reviewed. We will consider materials with inhomogeneities of any size, but our treatment is restricted to two-component materials. In Sec. II below we make a brief description of thin film optics. Here the transmittance and reflectance of a thin film are related to the dielectric and magnetic permeabilities of the film material. Some models of the dielectric permeability, which give insight into the physical phenomena involved, are also described. In Sec. III we treat the case of small inclusions of the components of the composite material. The effective dielectric permeability is then evaluated in the quasistatic approximation. We describe the rigorous bounds and effective medium theories that are valid in this limit, and consider cases where different amounts of information about the composite is known, namely the dielectric permeabilities and volume fractions of the constituents and isotropy of the structure. This leads to the Wiener,15 Hashin-Shtrikman16 and Bergman-Milton17,18 bounds. Simple effective medium theories for the dielectric permeability are applicable to special microstructures.

Recent advances in the characterization of composite materials have made it practical to incorporate more information about the geometry than the volume fractions and the condition of isotropy into rigorous bounds and effective medium theories. In Sec. IV we treat the situation when the pair and three-point correlation functions are known. This kind of theory has so far only been applied to certain cases, i.e., to fractal structures23 and random mixtures of hard24–26 or penetrable27 spheres in a matrix.

In Sec. V we treat the case of inhomogeneities with larger sizes, where the quasistatic approximation is not applicable. One may derive extended effective medium theories that describe some aspects of the optical properties in this case.19 However, when scattering is of importance a completely different approach is necessary, and radiative transfer or multiple scattering theory20–22 has to be used. It turns out that in many cases, e.g. when considering coatings, important simplifications can be made. A four-flux theory that is sufficiently accurate for comparisons with spectrophotometric data on inhomogeneous materials is described. Some final remarks are made in Sec. VI.

II THIN FILM OPTICS AND THE DIELECTRIC PERMEABILITY

When studying the optical properties of a material one generally measures the reflectance and transmittance as a function of wavelength and angle of incidence. These quantities are functions of the dielectric and magnetic permeabilities of the material. Conversely, it is possible to evaluate for example the dielectric permeability from carefully chosen combinations of experimental transmittance and reflectance data.28 In this section the theory of the optical properties of a thin film on a substrate is described. As a first step we consider light incident towards the boundary between two media denoted i and j. The angle to the surface normal is θi, as indicated in Fig. 1. The media are characterized by their complex dielectric and magnetic permeabilities, εi, j and μi, j. Part of the light is reflected at the boundary(rij) and part is transmitted (tij)) through the boundary. We distinguish between light with s-polarisation (E vectors normal to the plane spanned by the incident, reflected and transmitted beams) and with p-polarisation (H vectors normal to the same plane). From Maxwell’s equations, one can obtain the well known Fresnel’s relations for the reflected field amplitudes:29

Fig. 1 Definitions of symbols entering Fresnel’s relations.

(1)

(2)

(3)

(4)

Here ni and nj denote the refractive indices of the media; they are given by

(5)

and analogously for nj. Fresnel’s relations can be used to discuss the optical properties of a thin film on a substrate. We consider the geometry specified in Fig. 2 and let (2) denote the film (of thickness d) and (3) the substrate. A medium (1) surrounds the coated substrate. Further, we let (f) signify light incident from the frontside and (b) signify...

Produkt-Details

• Erscheint lt. Verlag: 22.10.2013
• Sprache: englisch
• Themenwelt: Naturwissenschaften ► Physik / Astronomie
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• Themenwelt: Technik ► Maschinenbau
• ISBN-10: 1-4832-8757-2 / 1483287572
• ISBN-13: 978-1-4832-8757-7 / 9781483287577