Thermal analysis of Micro, Nano- and Non-Crystalline Materials

Chemical kinetics provides mathematical models for explaining and predicting the transformation rate of a chemical system. The fundamental concept of chemical kinetics is based on the law of mass action established by Cato M. Guldberg (1836–1902) and Peter Waage (1833–1900) in the latter half of the nineteenth century (Waage P, Guldberg CM, Studies concerning affinity. Forhandlinger: Videnskabs – Selskabet i Christinia: 35, English trans. (1986) J Chem Edu 63(12):1044–1047, 1864; Guldberg CM, Waage P Concerning chemical affinity. J Prakt Chem [2]. 19:69, 1879), where equilibrium constants were derived in terms of kinetic data and rate equations. The two different aspects, that is, equilibrium and kinetics, were encountered by the recognition that chemical equilibrium is a dynamic process in which rates of reaction for the forward and backward reactions must be equal, so that the chemical driving force of the forward reaction is compensated by that of the reverse reaction. Because the respective reaction rates are proportional to the product of active masses of the reactant species, the equilibrium constant K can be represented by the ratio of the affinity constants (rate constants) of the forward and reverse reactions, k and k′: K = k/k′. The law of mass action was lately reintroduced by J.H. van’t Hoff (1852–1911) from the aspect of chemical kinetics (van’t Hoff JH, Etudes de dynamique chimique. Frederik Muller, Amsterdam, 1884).

Heat capacity is one of the essential thermophysical characteristics determining the thermal behavior of chemical substances. Its temperature dependence reflects all the excitations that the substance undergoes when heated. As such it relates to essential thermodynamic quantities such as (standard) enthalpy and entropy, which are used in thermodynamic descriptions of both stoichiometric compounds and their solutions. Considering the third law of thermodynamics defining absolute entropy, the heat capacity as a function of temperature represents, along with the enthalpy of formation, the only information necessary to specify the thermodynamic behavior of a stoichiometric compound at constant pressure by constructing the Gibbs energy function. It can be also used to evaluate the enthalpy of formation and entropy from high-temperature equilibrium data using the second law of thermodynamics.

There are numerous important personalities who paved the scientific road toward a better understanding of a state of glasses and who have become lost in the extended past of glassy research. Some of them are shown in the photographs below (Fig. 4.1), just to remember the illustrious history of glass exploration and their great protagonists (those responsible for the advanced understanding of glass crystallization, such as D.E. Day, I. Avramov, K.F. Kelton, L.A. Greer, T. Komatsu, C.T. Moynihan, J.W.P. Schmelzer, D.R. Uhlmann, M.C. Weinberg, E.D. Zanotto, and V.M. Fokin, were already portrayed in this book preface).

The glassy state is one of nonequilibrium and is characterized by a lack of long-range order. There are various parameters available for defining this state in a quantitative way, but it is important to appreciate that the glass transition temperature is not one of them. This distinction can be understood quite simply when one considers that the glass transition temperature represents, as the name suggests, the temperature at which the transition from an equilibrium state to the nonequilibrium glassy state occurs as a result of a restriction in the molecular mobility, corresponding to an increase in the average relaxation time (Rehage G, Borchard W, The thermodynamics of the glassy state. In: Haward RN (ed) The physics of glassy polymers. Applied Science Publishers, Barking, pp 54–107, 1973). It is because this glassy state is one of nonequilibrium that its structure can, and usually will, change continuously as a function of time even at constant temperature and pressure, in a process known as physical aging (Hutchinson JM, Physical aging of polymers. Prog Polym Sci 20:703–760, 1995). As a consequence, it is inappropriate to use the glass transition temperature, which is the temperature at which the glass was first formed, as a descriptor of the glassy state, except for the special case of the glassy state formed immediately after cooling.

Glasses are amorphous materials that lack the periodicity of crystalline substances. Structurally, they resemble metastable supercooled liquids but behave mechanically like solids. A typical way of preparing glass is by cooling a viscous supercooled liquid fast enough to avoid crystallization. Although this way of preparation is known for several thousands of years, the underlying molecular mechanism is not fully understood (Debenedetti PG, Metastable liquids. Concepts and principles. Princeton University Press, Princeton, 1996; Debenedetti PG, Stillinger FH, Supercooled liquids and the glass transition. Nature (Lond) 410:259–267, 2001).

Throughout the text, the subscripts _V , _p , and _T denote the isochronous, isobaric, or isothermal conditions, and the subscripts _cr, _l, or _g denote the crystalline, liquid, or glassy states. If the crystallization was suppressed (for example, by rapid cooling of the liquid below its melting temperature, T _m), a still equilibrium but metastable undercooled liquid state (ULS, subscripted as _ULS) characterized by an excess Gibbs free enthalpy G _exc(T) = G _ULS-cr(T) = G _ULS(T) − G _cr(T) and the liquid-like temperature dependence of G _ULS(T) is obtained below T _m (i.e., its heat capacity is C _p,ULS ∼ C _p,l).

Nucleation is the first step in the process leading to the phase transformation. In supercooled (supersaturated) liquid, nucleation and growth to macroscopic sizes would occur, but this process is restricted by some energy barriers and also by transport of molecules across the phase interface.

The crystal nucleation and growth taking place in glassy and/or amorphous states of solids are of technological importance for characterizing the kinetically controlled stability of the non-crystalline state and for fabricating glass-ceramics with desired properties (Strnad Z, Glass-ceramic materials. Elsevier, Amsterdam, 1986; Šestak J, Thermophysical properties of solids. Elsevier, Amsterdam, 1984). The real kinetics of the crystallization processes is fairly complicated, controlled by various factors of physical properties of glass (Šestak J, Mares JJ, Hubik P (eds), Glassy, amorphous and nanocrystalline materials. Springer, Dordrecht, 2011) and of physicochemistry of elemental kinetic processes. Enormous effort has been paid to formalize the fundamental kinetic theory for the complicated consecutive and/or concurrent processes of nucleation and growth. As one of the results, the overall kinetics of nucleation and growth was formalized as the well-known Johnson–Mehl–Avrami–Erofeyev–Kolgomorov (JMAEK) equation (Jacobs PWM, Tompkins FC, Classification and theory of solid reactions. In: Garner WE (ed) Chemistry of the solid state. Butterworth, London, 1955). The kinetic equation is widely applied for varieties of the solid-state transformation processes (Weinberg MC (ed), Ceramic transactions. Nucleation and crystallization in liquids and glasses, vol 30. The American Ceramic Society, Westerville, 1993; Galwey AK, Brown ME, Thermal decomposition of ionic solids. Elsevier, Amsterdam, 1999; Koga N, Tanaka H, A physic-geometric approach to the kinetics of solid-state reactions as exemplified by the thermal dehydration and decomposition of inorganic solids. Thermochim Acta 388:41–61, 2002). At the same time, the theoretical and practical validities of the application of JMAEK transformation kinetics to the respective processes are always open to discussion (Finney EE, Finke RG, Is there a minimal chemical mechanism underlying classical Avrami–Erofe’ev treatments of phase-transformation kinetic data? Chem Mater 21:4692–4705, 2009).

An attribute of amorphous/glassy state is that it is a solid state in which the atoms or molecules are not arranged in any long-range regular order. A glass is traditionally understood as the product obtained from a melted material that has been cooled at a sufficiently high cooling rate to obtain a rigid material without crystallization. The term amorphous is more general and encompasses not only the glasses but also non-crystalline substances prepared by other routes such as precipitation from solution, etc. Most solid materials can be prepared in the glassy/amorphous state, so that many branches of science are touched with the problem of amorphous-state properties, such as glass science, polymer science, metallurgy, biology, pharmaceutical science, and many other scientific disciplines.

The kinetic spotlight of crystallization has been studied to a large extent by preceding crucial studies, as well as by numerous papers published on the specific subject of metallic glasses within recent years. This chapter, however, provides no inventory attempt to assess all of them, although the metallic glasses remain as an intensely active area of research for reasons of various characteristic peculiarities of its crystallization kinetics. A new methodological approach for kinetic analysis has been practiced being based on the complexity of both the isothermal and the continuous heating modes. They are disproportional in its form of integral examination, where especially the Suriñach’s curve-fitting procedure was found useful and worth introduction and profitable employment. The crystallization kinetic parameters have been determined and followed by the concluding interpretation upon assuming certain mechanisms, which are deduced within the scope of both modes: the classical (nucleation and growth, abbreviated as JMAYK) and the alternative (normal grain growth, abbreviated as NGG) kinetic laws. Results are a part of a current systematic investigation of the thermodynamic stability and crystallization of the series of Pd–Si, Fe–Co–B, Fe–Si–B, and Al-based metallic glassy samples cast in the form of ribbons. Results have been generalized for a variety of rapidly quenched metallic ribbons from a binary metal–metalloid up to the multicomponent metallic alloys established in relationship to the kinetics of their crystallization. The as-quenched slices have been divided into two types, namely, the conventional metallic glasses and the multicomponent precursors for the nano-crystalline alloys.

Glassy materials lack the periodic atomic arrangements typical for crystals. They are by definition prepared by cooling a viscous glass-forming liquid fast enough to avoid crystallization. This way of preparation has been known for millennia and is used for the fabrication of conventional glassy products from such as windows panels and glass containers to more sophisticated materials such as bulk optical glasses for cameras and optical fibers that interconnect computer networks with recording devices, transmitting, and finally bringing the external world to our homes. Figure 14.1 shows the specific volume or enthalpy as a function of temperature for a typical glass-forming liquid.

Detailed information about crystallization kinetics is important for glass-ceramic (GC) production, which, in most cases, is based on controlled internal crystallization. In this context, kinetic parameters such as crystal nucleation rate and time-lag (or induction period) for nucleation are of great interest because they can be used to define the crystal number density, N (nuclei/m³), which in turn limits the maximal average size, \( {{\bar{R}}_{{{ \max }}}} \), of the crystals in the resulting microstructure. Both quantities determine, to a great extent, the properties and applications of GCs. The traditional method to estimate the number density of nucleated crystals (supercritical nuclei) consists of the development of these nuclei at a relatively high temperature (higher than the previous nucleation temperature) up to a detectable size by optical or electron microscopy (Fokin VM, Zanotto ED, Yuritsyn NS, Schmelzer JWP. J Non-Cryst Solids 352:2681, 2006). This method, developed by Gustav Tammann (Tammann’s method) more than 100 years ago to measure crystal nucleation rate in organic liquids (Tammann G. Z Phys Chem 25:441, 1898), was successfully applied to inorganic glasses for the first time by Ito et al. (Ito M, Sakaino T, Moriya T. Bull Tokyo Inst Technol 88:127, 1968) and Filipovich and Kalinina (Filipovich VN, Kalinina AM. Izv Akad Nauk USSR. Neorgan Mater 4:1532 (in Russian), 1968). It provides an estimation of the number of supercritical nuclei needed for the determination of the steady-state nucleation rate and the time-lag for nucleation. However, Tammann’s method is laborious because it includes image analysis of crystallized samples. The foregoing method is valid for the cases of stoichiometric (when crystal and glass have the same composition) and nonstoichiometric crystallization.

As all classic methods for kinetic analysis of data from thermal analysis experiments, the nonparametric kinetics method, NPK, assumes that the general expression for the reaction rate of a simple reaction iswhere g(α) symbolizes the kinetic model of the process and f(T) accounts for the temperature dependence of the reaction.

In this chapter we present and discuss experimental results on electron transport in various forms of granular diamond. Diamond has drawn attention in physical research as a semiconductor with unique properties. We should mention its extremely high thermal conductivity, resistance against radiation, wide bandgap, high mobility for electrons and holes, mechanical hardness, and biocompatibility giving diamond-based devices a potential applicability in a wide range of fields from high-power and high-frequency electronics to biomedicine. Preparation of synthetic diamond by high-pressure and high-temperature techniques in the 1950s was a first step to wide utilization. In the 1980s the chemical vapor deposition (CVD) technique was elaborated for diamond technology (Nebel CE, Ristein J (eds), Thin-film diamond I, II: semiconductors and semimetals, vols 76, 77. Elsevier, Amsterdam, 2004). From the late 1990s, the nano-crystalline and ultra-nano-crystalline diamond (NCD, UNCD) with a controlled grain size in the nanometer (nm) range came into play (Gruen DM, Annu Rev Mater Sci 29:211–259, 1999). Because of the possibility to prepare large-area thin films on non-diamond substrates, application of NCD and UNCD became promising.

Among the nanomaterials, glass-ceramics are expected to play a major role in future, especially with respect to optical applications. New properties, which cannot be achieved in homogeneous glasses, should enable challenging applications, such as up-conversion glasses that enable the transformation of light with larger wavelength to light of shorter wavelength, for example, of near-infrared light to green light (Jacinto et al., Opt Soc Am B 26:1002–1007, 2009; Wang and Ohwaki, J Appl Phys Lett 63:3268–3270, 1993). A prerequisite for optical applications is that the glass-ceramics are transparent for light of the respective wavelength. Hence, the crystallites must be small and the crystal size distribution narrow. Besides up-conversion materials, also materials that show distinct fluorescence properties find wide applications. Among these, especially glass-ceramics for the conversion of the light emitted by blue light-emitting diodes (LEDs) to white light are to be mentioned (He and Zheng, Opt Lett 35:2955–2957, 2010; Zakanskas et al., J Phys D 35:354006, 2010). For higher light density, the heat removal of composites consisting of inorganic phosphors embedded in organic polymers is scarcely possible. Devices with much higher thermal conductivity are obtained when the inorganic phosphors are directly crystallized from glasses because the residual glassy matrix has a much higher thermal conductivity than the polymer. Another important field is the precipitation of ferrites (Woltz and Rüssel, J Non-Cryst Solids 337:226–231, 2004) or semiconducting phases from borate glasses (Garkova et al., J Non-Cryst Solids 320:291–298, 2003). In the latter case, the glasses are subsequently dissolved in water or acid and finally nano-crystalline powders with a narrow crystal size distribution are obtained (Woltz and Rüssel, J Non-Cryst Solids 337:226–231, 2004). These nano-crystalline powders possess interesting magnetic, electrical, or optical properties.

It is well known that the existence of the energy barrier of nucleation is a result of the interplay of two antagonistic tendencies: an endeavor of the system to go from initial metastable phase to a more favorable one, and a general trend to minimize the area of interfaces between different phases in the system. The former leads to a negative volume contribution \( \Delta {G_{\text{V}}} \) to the total Gibbs free energy of the cluster formation \( \Delta G \), whereas the latter corresponds to the positive surface contribution \( \Delta {G_{\text{S}}} \):where \( \Delta \mu \) is the difference of the chemical potentials of the initial metastable and the newly growing phases, n is the number of building units in the cluster, σ is the excess surface energy, and γ stands for the shape factor, which describes the ratio of the surface area of the cluster to its volume.

Batches made with a variety of precursors were subjected to thermogravimetric analysis. The baseline modifications included an all-nitrate batch with sucrose addition, an all-carbonate batch, and batches with different sources of alumina. All batches were formulated for a single glass composition (a vitrified, simulated, high-alumina, high-level waste). Batch samples were heated from ambient temperature to 1,200°C at constant heating rates ranging from 1 to 50 K/min. Major gas-evolving reactions began at temperatures just above 100°C and were virtually complete by 650°C. Activation energies for major reactions were obtained with the Kissinger method. A rough model for the overall kinetics of the batch conversion was developed to be eventually applied to a mathematical model of the cold cap.

The escalation of thermochemical research in the 1990s became a main engine in the search for yet new sorts of ceramic superconducting material, generally called the high-T _c superconductors (HTSC), with a transition temperature (T _c) far above the boiling temperature of nitrogen (77 K). Although the research boom has gradually expired, the commercial applications missed the initially promised contractions of magnetically levitated trains, powerful electric motors, or superefficient power transmission. However, thermal analysis evidently played a significant role, so that it became also reflected in extended publication activity in relevant journals, not excluding Thermochimica Acta and Journal of Thermal Analysis. The progress of HTSC was associated with better understanding of phase diagrams, starting from the oxide (Cu, Ba, Y), their binaries through pseudo-binaries to the Y–Ba–Cu–O pseudo-ternaries, yielding an improvement in the construction of phase diagrams. The research finally moved to the novel families of HTSC in the Bi–Ca–Sr–Cu–O systems and the determination of their thermodynamic properties. Increased attention was paid to the improvement of calculation methods and simulation procedures of the phases involved, and finally a series of improved thermodynamic data was published (Table 22.1).