**Crystallization Kinetics of Amorphous Materials**

Miray Çelikbilek, Ali Erçin Ersundu and Süheyla Aydn *Istanbul Technical University* 

*Turkey* 

#### **1. Introduction**

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applied in the kinetics analyses of solid state decompositions (crystolysis

Amorphous (non-crystalline) materials have no crystal structure where the atoms appear to have a random distribution (Omar, 1993). There are different classes of amorphous materials. Glasses, inorganic materials which have no long-range order (<10 Å) and high viscosity greater than 1013 Poise, are the most typical amorphous materials (Doremus, 1973; Jackson, 2004; Park, 2009). The regular arrangement resulting from the distribution over long distances of a repeating atomic arrangement, which is characteristic of a crystal, is missing in glasses (see Fig. 1). However, there is often evidence of a short-range order in glasses, which corresponds to the atomic arrangement in the immediate vicinity of any selected atom (Carter & Norton, 2007).

Fig. 1. Schematic two-dimensional illustration of the atomic arrangement in (a) crystal and (b) glass (Carter & Norton, 2007)

Glass can be formed by cooling from a liquid state without a change in its specific volume, which delays crystallization and assist to reach the glass transition temperature before the crystallization occurs (Jackson, 2004; Park, 2009). This is why amorphous materials, such as glasses, are sometimes referred to as supercooled liquids (Omar, 1993).

In a liquid, the atoms or molecules move around much more rapidly than in a crystal. They are constantly in motion, jiggling around relative to each other, unlike in a crystal, where the

Crystallization Kinetics of Amorphous Materials 129

former. Among various oxides used in the industrial materials, SiO2, GeO2, B2O3, and P2O5 are known to be good network formers which can develop the three-dimensional random

Fig. 3. Schematic two-dimensional illustration of the structure of a binary sodium silicate

The special glasses used as key components of various devices in the fields of optics, electronics, and opto-electronics are not always silicates but are often non-silicate glasses of the phosphate, borate, germanate, vanadate or tellurite systems. Although non-silicate glasses are not generally applied to mass production due to the high cost of raw materials and their rather inferior chemical durability, they do show unique properties that cannot be obtained for silicate glasses (Yamane & Ashara, 2000). Comparing with silicate, borate and phosphate glasses, tellurite glasses have drawn considerable attention because of their various promising properties, such as relatively low-phonon energy, high linear and nonlinear refractive index, high dielectric constant, good infrared transmission, good corrosion resistance, thermal and chemical stability, low crystallization ability and easy fabrication at low temperatures. Therefore, tellurite glasses are of scientifically and technologically important for their potential use in fiber optics, laser hosts, infrared and infrared to visible upconversion applications in optical data storage, sensors, and spectroscopic applications. TeO2 is a conditional glass former which does not transform to the glassy state under normal quenching conditions. Therefore, addition of a secondary component, such as heavy metal oxides, alkalis or halogens increases its glass forming ability (Çelikbilek et al., 2010, 2011a, 2011b; El-Mallawany, 2002; Ersundu et al., 2010a, 2010b, 2011; Karaduman et

In order to use special glasses in the fields of opto-electronics at high optical intensities without exposure to thermal damage it is important to recognize their physical and thermal characteristics and also to control the crystallization processes. The investigation of crystallization in terms of kinetics is an important informational tool for the audience and

glass (Yamane & Ashara, 2000)

al., 2011).

network and can form a glass by themselves (Yamane & Ashara, 2000).

atoms are bound to specific lattice sites. When a liquid is cooled, the space for the atoms to move around decreases and on further cooling below the glass transition temperature, the atoms can no longer move around with respect to each other, and so the material becomes a solid. A measure of this is the specific volume, which can be measured as the difference between the density of the crystal and of the liquid. As a glass-forming material cools, this excess volume decreases, and finally the density of the glass approaches that of the crystal, as illustrated in Fig. 2. In practice, the formation of an amorphous or crystalline solid depends on how rapidly the liquid is cooled through the glass transition temperature (Jackson, 2004). Upon cooling the liquid, if there is a discontinuity in volume change or in rate of cooling the liquid crystallizes, however if the liquid passes into a supercooled state the volume decreases and no crystallization occurs (Carter & Norton, 2007).

Fig. 2. The specific volume in a liquid decreases more rapidly with temperature than the crystal. The thermal expansion coefficient of glass is similar to that of the crystal. The final specific volume of the glass depends on the cooling rate: (a) fast cooling, (b) normal cooling, (c) slow cooling (Carter & Norton, 2007; Jackson, 2004)

It is believed that most materials can be prepared as glasses by sufficiently rapid quenching but there is a notable exception: no pure metal has been prepared in an amorphous state (Jackson, 2004). Materials which can form non-crystalline solids with the atomic arrangement shown in Fig. 1b and at an appreciable size are found in glass systems in oxides, halides, and chalcogenides. The three-dimensional random network of strong bonds is developed by the constituent called the "network former". In principle, glass formation is possible for a system of any composition provided if it contains sufficient of the network former. Network modifiers can also participate in glass formation by acting to modify the glass properties. These components do not form networks but occupy thermodynamically stable sites as illustrated schematically in Fig. 3 or act as a replacement for a part of network

atoms are bound to specific lattice sites. When a liquid is cooled, the space for the atoms to move around decreases and on further cooling below the glass transition temperature, the atoms can no longer move around with respect to each other, and so the material becomes a solid. A measure of this is the specific volume, which can be measured as the difference between the density of the crystal and of the liquid. As a glass-forming material cools, this excess volume decreases, and finally the density of the glass approaches that of the crystal, as illustrated in Fig. 2. In practice, the formation of an amorphous or crystalline solid depends on how rapidly the liquid is cooled through the glass transition temperature (Jackson, 2004). Upon cooling the liquid, if there is a discontinuity in volume change or in rate of cooling the liquid crystallizes, however if the liquid passes into a supercooled state

the volume decreases and no crystallization occurs (Carter & Norton, 2007).

Fig. 2. The specific volume in a liquid decreases more rapidly with temperature than the crystal. The thermal expansion coefficient of glass is similar to that of the crystal. The final specific volume of the glass depends on the cooling rate: (a) fast cooling, (b) normal cooling,

It is believed that most materials can be prepared as glasses by sufficiently rapid quenching but there is a notable exception: no pure metal has been prepared in an amorphous state (Jackson, 2004). Materials which can form non-crystalline solids with the atomic arrangement shown in Fig. 1b and at an appreciable size are found in glass systems in oxides, halides, and chalcogenides. The three-dimensional random network of strong bonds is developed by the constituent called the "network former". In principle, glass formation is possible for a system of any composition provided if it contains sufficient of the network former. Network modifiers can also participate in glass formation by acting to modify the glass properties. These components do not form networks but occupy thermodynamically stable sites as illustrated schematically in Fig. 3 or act as a replacement for a part of network

(c) slow cooling (Carter & Norton, 2007; Jackson, 2004)

former. Among various oxides used in the industrial materials, SiO2, GeO2, B2O3, and P2O5 are known to be good network formers which can develop the three-dimensional random network and can form a glass by themselves (Yamane & Ashara, 2000).

Fig. 3. Schematic two-dimensional illustration of the structure of a binary sodium silicate glass (Yamane & Ashara, 2000)

The special glasses used as key components of various devices in the fields of optics, electronics, and opto-electronics are not always silicates but are often non-silicate glasses of the phosphate, borate, germanate, vanadate or tellurite systems. Although non-silicate glasses are not generally applied to mass production due to the high cost of raw materials and their rather inferior chemical durability, they do show unique properties that cannot be obtained for silicate glasses (Yamane & Ashara, 2000). Comparing with silicate, borate and phosphate glasses, tellurite glasses have drawn considerable attention because of their various promising properties, such as relatively low-phonon energy, high linear and nonlinear refractive index, high dielectric constant, good infrared transmission, good corrosion resistance, thermal and chemical stability, low crystallization ability and easy fabrication at low temperatures. Therefore, tellurite glasses are of scientifically and technologically important for their potential use in fiber optics, laser hosts, infrared and infrared to visible upconversion applications in optical data storage, sensors, and spectroscopic applications. TeO2 is a conditional glass former which does not transform to the glassy state under normal quenching conditions. Therefore, addition of a secondary component, such as heavy metal oxides, alkalis or halogens increases its glass forming ability (Çelikbilek et al., 2010, 2011a, 2011b; El-Mallawany, 2002; Ersundu et al., 2010a, 2010b, 2011; Karaduman et al., 2011).

In order to use special glasses in the fields of opto-electronics at high optical intensities without exposure to thermal damage it is important to recognize their physical and thermal characteristics and also to control the crystallization processes. The investigation of crystallization in terms of kinetics is an important informational tool for the audience and

Crystallization Kinetics of Amorphous Materials 131

But when the particle of radius *r* is formed, there is another energy term to be considered,

∆*Gs* = 4π*r*2γ (7)

The first of these terms involves the increase in energy required to form a new surface. The second term is negative and represents the decrease in Gibbs free energy upon solidification. Because the first is a function of the second power of the radius, and the second a function of the third power of the radius, the sum of the two increases, goes through a maximum, and

Fig. 4. The free energy change associated with homogeneous nucleation of a sphere of radius *r* 

The radius at which the Gibbs free energy curve is at maximum is called the critical radius *r*\*, for a nucleus of solid in liquid. The driving force of the Gibbs free energy will tend to cause a particle with a smaller radius than *r*\* to decrease in size. This is a particle of subcritical size for nucleation. A viable nucleus is one with radius greater than or equal to *r*\*. The critical Gibbs free energy corresponding to the radius *r*\* is ∆*G*\*. These terms can be

<sup>3</sup> <sup>π</sup>*r*3∆*G*v (8)

the surface energy. The surface energy of the particle is:

where γ = γs-l the surface energy between solid and liquid.

<sup>∆</sup>*G*<sup>r</sup> <sup>=</sup> <sup>4</sup>π*r*2γ + <sup>4</sup>

The sum of the two energy term is:

then decreases (Fig. 4).

(Ragone, 1994)

shown to be:

therefore this chapter "Crystallization Kinetics of Amorphous Materials" is crucial to have a complete understanding of the crystallization phenomenon.
