**1.1 Optical principles of pearl luster and interference pigments**

The physical background of optical interference effects has been the subject of many publications [1.1-1.4, 1.6–1.9]. The optical principles of pearl luster (interference) pigments are shown in Figure 1.2 for a simplified case of nearly normal incidence without multiple reflection and absorption. At the interface P1 between two materials with refractive indices *n*1 and *n*2, part of the beam light L1 is reflected (L1) and part is transmitted (i.e., refracted) (L2). The intensity ratios depend on *n*1 and *n*2. In a multilayer arrangement, as found in pearl or pearl luster and iridescent materials (Figure 1.1D), each interference produces partial reflection. After penetration through several layers, depending on the size of and difference between *n*1 and *n*2, virtually complete reflection is obtained, provided that the materials are sufficiently transparent.


\*Instead of mica other platelets such as silica, alumina, or borosilicate can be used.

Table 1.1. Overview of inorganic effect pigments (1.12)

Ceramic Coatings for Pigments 241

In practice, platelet crystals are synthesized with a layer thickness *d* calculated to produce the desired interference colours (iridescence). Most pearl luster pigments now consist of at

Thin flakes (thickness ca. 500 nm) of a material with a low refractive index (mica, silica, alumina, glass) are coated with a highly refractive metal oxide (TiO2, Fe2O3, layer thickness ca. 50–150 nm). This results in particles with four interfaces that constitute a more complicated but still predictable thin film system. The behavior of more complex multilayer pigments containing additional, thin, light-absorbing films can also be calculated if

Colour effects depend on the viewing angle. Pearl luster pigment platelets split white light into two complementary colours that depend on the platelet thickness. The reflected (interference) colour dominates under regular (maximum) reflection, i.e., when the object is observed at the angle of regular reflection. The transmitted part dominates at other viewing angles under diffuse viewing conditions, provided that there is a non-absorbing (white) or

Variation of the viewing angle therefore produces a sharp gloss (reflectance) peak, and the colour changes between two extreme complementary colours. The resulting complex interplay of luster and colour is measured goniophotometrically in reflection and at different angles. A pearl luster pigment is characterized by a minimum of three L\*a\*b\* data sets (CIE L\*a\*b\* system) measured under different conditions (e.g., 0°/45° black background, 22.5°/22.5° black background, 0°/45° white background). An analysis of these data specifies a pigment on the

**2. Application of the Taguchi method to develop a robust design for the** 

For a long time beautiful and deep pearlescent pigments have attracted human attention and have been used in many cases [2.1]. These pigments consist of thin transparent small

least three layers of two materials with different refractive indices.

basis of its hiding power, luster, and hue [1.1, 1.10, 1.11, 1.12].

**synthesis of mica-SnO2 gold pearlescent pigment** 

**Material Refractive index**  Vacuum/Air 1.0 Water 1.33 Proteins 1.4 Organic polymers (plastics, Lacquers, etc.) 1.4-1.7 Mica 1.5 CaCO3 (aragonite) 1.68 Natural pearl (guanine, hypoxanthine) 1.85 Pb(OH)2 . 2PbCO3 2.0 BiOCl 2.15 TiO2 (anatase) 2.5 TiO2 (rutile) 2.7 Fe2O3 (hematite) 2.9

Table 1.2. Refractive indices of materials.

appropriate optical parameters are known.

reflecting background.

**2.1 Introduction** 

Fig. 1.2. Simplified diagram showing nearly normal incidence of a beam of light (L1) from an optical medium with refractive index *n*1 through a thin solid film of thickness *d* with refractive index *n*2. L1 and L2 are regular reflections from phase boundaries P1 and P2. L3 represents diffuse scattered reflections from the transmitted light.

In pigments that simulate natural pearl effects, the simplest case is a platelet shaped particle with two phase boundaries P1 and P2 at the upper and lower surfaces of the particles, i.e., a single, thin, transparent layer of a material with a higher refractive index than its surroundings. For small flakes with a thickness of ca. 100 nm, the physical laws of thin, solid, optical films apply.

Multiple reflection of light on a thin solid film with a high refractive index causes interference effects in the reflected light and in the complementary transmitted light. For the simple case of nearly perpendicular incidence, the intensity of the reflectance depends on the refractive indices (*n*1, *n*2), the layer thickness (d), and the wavelength (λ):

$$\begin{aligned} I &= \frac{A^2 + B^2 + 2AB\cos\Theta}{1 + A^2B^2 + 2AB\cos\Theta} \\\\ \text{Where } A &= \frac{n\_1 - n\_2}{n\_1 - n\_2}, \quad B = \frac{n\_2 - n\_1}{n\_1 - n\_2}, \quad \Theta = 4\pi \frac{n\_2}{n\_2} \end{aligned}$$

With given *n*1 and *n*2 the maximum and minimum intensities of the reflected light, seen as interference colours, can be calculated and agree well with experimental results. Values for the refractive indices of the most important materials for pearl luster pigments are shown in Table 1.2.

Fig. 1.2. Simplified diagram showing nearly normal incidence of a beam of light (L1) from an

In pigments that simulate natural pearl effects, the simplest case is a platelet shaped particle with two phase boundaries P1 and P2 at the upper and lower surfaces of the particles, i.e., a single, thin, transparent layer of a material with a higher refractive index than its surroundings. For small flakes with a thickness of ca. 100 nm, the physical laws of thin,

Multiple reflection of light on a thin solid film with a high refractive index causes interference effects in the reflected light and in the complementary transmitted light. For the simple case of nearly perpendicular incidence, the intensity of the reflectance depends on

With given *n*1 and *n*2 the maximum and minimum intensities of the reflected light, seen as interference colours, can be calculated and agree well with experimental results. Values for the refractive indices of the most important materials for pearl luster pigments are shown in

the refractive indices (*n*1, *n*2), the layer thickness (d), and the wavelength (λ):

optical medium with refractive index *n*1 through a thin solid film of thickness *d* with refractive index *n*2. L1 and L2 are regular reflections from phase boundaries P1 and P2. L3

represents diffuse scattered reflections from the transmitted light.

solid, optical films apply.

Table 1.2.


Table 1.2. Refractive indices of materials.

In practice, platelet crystals are synthesized with a layer thickness *d* calculated to produce the desired interference colours (iridescence). Most pearl luster pigments now consist of at least three layers of two materials with different refractive indices.

Thin flakes (thickness ca. 500 nm) of a material with a low refractive index (mica, silica, alumina, glass) are coated with a highly refractive metal oxide (TiO2, Fe2O3, layer thickness ca. 50–150 nm). This results in particles with four interfaces that constitute a more complicated but still predictable thin film system. The behavior of more complex multilayer pigments containing additional, thin, light-absorbing films can also be calculated if appropriate optical parameters are known.

Colour effects depend on the viewing angle. Pearl luster pigment platelets split white light into two complementary colours that depend on the platelet thickness. The reflected (interference) colour dominates under regular (maximum) reflection, i.e., when the object is observed at the angle of regular reflection. The transmitted part dominates at other viewing angles under diffuse viewing conditions, provided that there is a non-absorbing (white) or reflecting background.

Variation of the viewing angle therefore produces a sharp gloss (reflectance) peak, and the colour changes between two extreme complementary colours. The resulting complex interplay of luster and colour is measured goniophotometrically in reflection and at different angles. A pearl luster pigment is characterized by a minimum of three L\*a\*b\* data sets (CIE L\*a\*b\* system) measured under different conditions (e.g., 0°/45° black background, 22.5°/22.5° black background, 0°/45° white background). An analysis of these data specifies a pigment on the basis of its hiding power, luster, and hue [1.1, 1.10, 1.11, 1.12].
