Advances in Combustion Synthesis and Technology

By Bentham Science Publishers

This reference is an accessible update on combustion synthesis and the chemical technology for synthesizing composite materials. Nine chapters offer an overview of the subject with recent references, giving the reader an informed perspective.

The book starts with an introduction to thermodynamic models used in combustion synthesis. Subsequent chapters explain the application of combustion synthesis to manufacture different materials such as nanostructured non-ferrous alloys, ceramic powders, functionally graded materials, boron carbide-based superhard materials, shape memory alloys, biomaterials, high-entropy alloys and rare earth phosphates.

The range of topics makes this book a useful guide for students, scientists and industrial professionals in the field of chemical engineering, metallurgy and materials science.

• Language: English
• Publisher: Bentham Science Publishers
• Release date: Mar 21, 2022
• ISBN: 9789815050448

Book preview

Thermodynamic Modeling Of Combustion Synthesis

Murat Alkan¹, *, Esra Dokumaci Alkan¹

¹ Department of Metallurgical and Materials Engineering, Dokuz Eylul University Faculty of Engineering, Tinaztepe Campus, 35390, Buca – Izmir, Turkey

Abstract

This paper describes a summary of the basis of the thermodynamic variab-les with their equations, the thermodynamic models with their equations, the thermodynamic modeling software with their databases, the thermodynamic background of the combustion synthesis (CS) process with some examples. The integral molar Gibbs free energy change of mixing (ΔGM) is the most important thermodynamic quantity. There are several models to calculate and minimize ΔGM. The calculation of ΔGM can be very difficult if there are several components in the identified process. The thermodynamic computer packages (software and their databases) enable the calculation of complex equations with high accuracy. Adiabatic temperature (Tad) is one of the parameters essential for the self-propagation of combustion synthesis. The comparison of the most common thermodynamic modeling software was introduced in this study. The results of some of the experimental studies about the CS process were also given in the concept of this study.

Keywords: Adiabatic temperature, Combustion synthesis, Gibbs energy minimization, Thermodynamic models, Thermodynamic software.

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* Corresponding author Murat Alkan: Department of Metallurgical and Materials Engineering, Dokuz Eylul University Faculty of Engineering, Tinaztepe Campus, 35390, Buca – Izmir, Turkey; Tel:[phone] Fax: [phone] E-mail: [e-mail]

FUNDAMENTALS OF METALLURGICAL THERMODYNAMICS AND THERMODYNAMICS OF SOLUTIONS

Thermodynamics is related to energy and energy transformation. Thermodynamics only focuses on the equilibrium states, so it doesn’t study the systems that have time-dependent changes. If a system with a time-dependent change will be investigated, the calculations of thermodynamic variables can be done with the support of thermodynamic models. In an open system, both matter and energy transfers can be realized between the system and its surroundings. In an adiabatic system, only energy transfer occurs between the system and its surroundings. In an isolated system, neither energy nor matter is transferred [1, 2].

The first law of thermodynamics is about the conservation of energy: if the mass of a system is constant, the total energy cannot be created or destroyed; it can only be converted from one form to another form. As a state function, the internal energy (U) equals to differences between the heat (q) transferred into the system and the work (w) done by the system. But, the state functions do not have any absolute values. Only the value changes between two exact states (initial and final states) can be calculated. This relation can be formulated as eq. (1). The second law of thermodynamics is derived when there is a lack of transformation of heat into work that occurred. A state function called entropy (S) is defined from this law. In a closed system, the entropy cannot decrease, it increases during irreversible processes while it remains constant for reversible processes. For any processes, the total entropy changes (dStot) are equal to the sum of the entropy of the system (dSsys) and surroundings (dSsurr) given in eq. (2). For a reversible process, the entropy changes between two exact states (initial and final states) can be calculated as eq. (3). The entropy of a system is also defined by the statistical thermodynamics with Boltzmann’s equation, given in eq. (4) where kB is Boltzmann’s constant and W is a measure of the probability of a system [1-6].

The enthalpy (H) is extensive state property, and it can be explained as the sum of the system’s internal energy (U) and multiplication of pressure (P) with volume (V) of the system as eq. (5). If the pressure of the system is constant in both the initial and the final states, the enthalpy change equals heat exchange. If a process is carried out at constant pressure, an increase in the enthalpy change means the absorbing of the heat, eq. (6). The heat capacity (C) of a system can be described as the ratio of the heat to the change in the absolute temperature. If the system is at constant pressure, the heat capacity (CP) can be calculated as eq. (7). The Gibbs free energy change (dG) describes if a reaction is spontaneous or not. In a closed system, the Gibbs free energy changes can be calculated as eq. (8), where the temperature and pressure of the system are constant. If the dG value is negative, the mentioned reaction will be spontaneous. If the dG value is equal to zero, then the mentioned reaction is in equilibrium and is reversible [1-6].

The thermodynamics of solutions is related to vapor pressure, absolute temperature, and molar amount of the components of a solution. The partial thermodynamic extensive quantities of any components are important in solution thermodynamics and these values can be calculated as eq. (9), by taking the partial derivatives of the extensive quantities (Z) with respect to the amount of the component added into the solution. Any thermodynamic extensive quantity of a solution can be calculated mathematically. For instance, the Gibbs free energy of a solution (GM) is the sum of the Gibbs free energies of pure components in the solution (G°), the Gibbs free energy of ideal solution (Gid), and the excess Gibbs free energy of solution (Gxs), eq. (10). The change in the integral Gibbs free energy of solution (ΔGM) is calculated by the sum of the partial molar Gibbs free energy changes of a component multiplied by its molar fraction (Xi), eq. (11). The activity of a component in a solution (ai) is calculated by the ratio of partial pressure of the component in the solution (pi) to the partial pressure of the component at its pure state (pi°), eq. (12). The change in the integral Gibbs free energy of solution can also be calculated by means of the activity values of the component, eq. (13), where R is the universal gas constant, T is the absolute temperature, Xi is the molar fraction of the component, and ai is the activity of the component. If the activity of a component is equal to its mole fraction, the solution behaves ideally. If the solution is not ideal, the ratio between the activity (ai) and a molar fraction (Xi) of a component gives the activity coefficient of the component (γi) in the solution, eq. (14). An excess thermodynamic function can be calculated from the differences between the state function values and the ideal state values. The excess molar Gibbs free energy of solution can be calculated by eq. (15) [7-9].

There are three common methods for experimental measurements of thermodynamic quantities: calorimetric technique, vapor pressure measurement, and electrolysis. Calorimeters can be utilized to calculate the thermodynamic values of pure components. Calorimeters are also used to determine the integral and partial enthalpy changes of a solution. However, this technique isn’t suitable for the calculation of the partial Gibbs free energy changes and activities of the components. The activity value of a component can be calculated by measuring the vapor pressure of the component in the solution. The partial Gibbs free energy changes are also calculated by using an electrolysis cell. The electromotor force (EMF) can be measured, and due to the Nernst Equation, eq. (16), the Gibbs free energy, the standard Gibbs free energy, and the activity value of a component in the solution can be determined. In eq. (16), z is the number of electrons transferred, F is the Faraday constant, and E is the electromotor force of the cell. The partial enthalpy and entropy changes can also be measured by using EMF values [10].

THERMODYNAMICS OF COMBUSTION SYNTHESIS

For the thermodynamic investigation of a combustion synthesis (CS) reaction, different states can be utilized: stationary, equilibrium, reversibility, and stability. The stationary state means that the characteristics of a system stay constant and independent from duration. A CS reaction is started with initiation, and the reaction is propagated simultaneously. The basis of the driving force of a CS reaction is the ability to convert the chemical potential of the system into heat energy. The initiation begins with the increase of the initial temperature up to a critical level, where the rate of reciprocal diffusion of reactants is appropriate to start a chemical reaction. Due to the exothermic reaction, the temperature of the system will increase rapidly, and the reaction rate will increase. This self-propagating process will be done when the system approaches a new steady state. It is impossible for the system to relapse its initial state from this new steady-state spontaneously [11].

For the system definition of a CS process, the specific duration of reaction, combustion and cooling must be investigated. The rate of the chemical reaction is very fast (0.001-0.1 s), and there is not enough time for heat exchange between the system and its surrounding. So, the chemical reaction can be assumed as an isolated system. The completion of combustion wave propagation also takes place fast (1-10 s). The cooling duration is connected with the heat losses of the system. If the heat loss is lower, then the cooling will take place longer (100-1000 s). Due to this long duration, the process cannot be assumed as an isolated system. The starting state of the CS processes, before the initiation, is named the non-equilibrium quasi-stationary state. Because the free energy is not at its minimum value and the system parameters do not change during a long duration. After initiation, the free energy of the system is reduced and a more equilibrium state can be obtained. In the final state, when the cooling is finished, the system approaches a new equilibrium. In the combustion synthesis process, the final state is always more stable than its initial state [11].

In a combustion synthesis process, the thermodynamic calculations are realized to predict the adiabatic combustion temperature (Tad) and the final products. The adiabatic combustion temperature means the highest temperature which the reaction products can reach when the reaction energy is only utilized to heat the product under adiabatic conditions. The reaction energy, or the heat of the reaction (Q), is calculated by the standard enthalpy of formation differences between the reactants and products, eq. (17). If there is no phase transformation in the products, Tad is easily calculated by getting the integration of the heat capacities of the products (CP), eq. (18). If there are phase transformations (melting, boiling, allotropic trans., etc.) that occurred in the products, their energy requirements must also be considered during Tad calculation. The latent heat required for the phase transformation of a product (∆H°LH) at the transition temperature (Ttr.<Tad) , and the standard enthalpy changes of the transformed product between Ttr. and Tad (∆H°tr.) must be subtracted from the heat of the reaction depending on the molar fraction of the transformed product (Xtr.). If there is more than one phase transformation, the sum of the latent heat and the standard enthalpy changes of all transformed products must be used for Tad calculation, eq. (19) [12].

Tad calculation is dependent on the final products. So, assumptions about which products will be obtained must be made before Tad calculations. Tad calculation and its equation are more complex if a multi-component system is observed. Because the final products are wide open. Hence, the final products must be investigated firstly, and then Tad calculation can be done. There are several computer-based software programs and their database to determine the final products at the equilibrium and to calculate Tad of the system [12].

Thermo-gravimetric analysis (TGA), differential thermal analysis (DTA), and differential scanning calorimetry (DSC) are the most common methods for detecting the thermodynamic quantities for a combustion synthesis. These methods support measuring the transformation temperatures of the compounds, the starting temperature of a CS reaction, the produced energy during a CS reaction, and the kinetic observation of a CS reaction [13].

COMMONLY USED THERMODYNAMIC MODELS

There are several models to define the thermodynamic variables of different phases. The integral Gibbs free energy changes are commonly utilized for modeling the thermodynamic properties because of the ability to get more experimental data than the others. The Gibbs free energy value of a phase depends on two key aspects: bonding energies of the components and their configuration. The physical and chemical properties of a phase (unit structure, bonding type, order-disorder arrangement, etc.) affect the model selection. The unit structures of phases can be divided into sublattices, which have different crystallographic symmetries and numbers of atoms. The sublattices may contain not only one kind of component but also several kinds of components. There are at least two compounds in a solution phase, and they are named the end-members of the solution. The solubility is based on these end-members [14]. The Gibbs free energy function for a pure phase and end-members is given in eq. (20) at a given temperature and pressure. The Gibbs free energy changes of mixing is given in eq. (21) for the molecular model. In eq. (21), Gi represents the Gibbs free energy of an end-member i. The expression of the excess Gibbs free energy of mixing can be given as a function of molar fractions of end-members and the mixing parameters between two end-members (Lni,j), eq. (22) [15].

The Gibbs free energy changes of mixing are given in eq. (23) for the sublattice model. In eq. (23), Yis represents the molar fraction of ith component on sublattice s, and αs represents the number of sites on sublattice s per mole of phase. The excess Gibbs free energy of mixing is given in eq. (24) for the sublattice model. The binary interaction parameters (Lsi,j) is also given in eq. (25). The higher-order (ternary, quaternary, etc.) interaction parameters make Gxs term be more complex [15].

Single-Lattice Random-Mixing Models

The random-mixing or Bragg-Williams models describe that the constituents are randomly placed over the lattice without any connection and repetition. The configurational entropy change of mixing is connected with the randomly positioned constituents on the lattice. This is also called the ideal molar entropy changes of mixing, eq. (26). If the molar enthalpy change of the mixing is zero and the molar entropy change of mixing equals the configurational entropy change, this solution can be named as an ideal Raoultian Solution. The molar Gibbs free energy change of ideal mixing is given in eq. (27). If the molar enthalpy change of mixing and the excess molar Gibbs free energy of mixing in a binary system are a parabolic function of the molar fraction of the constituents where the non-configurational molar entropy change of mixing is also zero, this solution can be named as a regular solution [16].

The excess molar Gibbs free energy of mixing can be written as a polynomial expansion of an alpha-function (α12), eq. (28). The alpha-function has coefficients that depend on temperature but do not depend on compositions, eq. (29). If i is zero, Gxs will be equal to ⁰L12X1X2 and this solution will be regular. If i is one, Gxs will be equal to X1X2(⁰L12 + ¹L12 (X1–X2)) and this solution will be sub-regular. The expression of (X1–X2)i is named as Redlich-Kister polynomials [16].

The excess molar Gibbs free energy of mixing values in multicomponent systems can be evaluated by their binary subsystems. There are several geometrical models suggested for the ternary systems. The Kohler and the Maggianu models are symmetrical models. The Kohler/Toop and the Muggianu/Toop models are asymmetrical models. In every model, Gxs value of a ternary solution (has a composition point of p) is projected by using Gxs values of three binary subsystems (have the composition points of a, b and c). Gxs value of the ternary solution can be calculated as a function depending on the binary alpha-functions, eq. (30). If two of the components in a ternary system are chemically similar, using an asymmetrical model is more suitable. For a dilute ternary solution, the Kohler model is more suitable than the Maggianu model. When the amount of component is increased, the accuracy of the estimation of the thermodynamic properties also increases. The calculation of the thermodynamic properties in a solution containing several dilute solutes can also be possible. The activity coefficient of a dilute solute (γi) can be calculated as given in eq. (31), where γi° is the limiting Henrian activity coefficient of a dilute solute and ɛij is the first-order interaction parameter [16].

Multiple-Sublattice Random-Mixing Models

There are often two or more sublattices in several compounds and solutions. Specific atoms tend to occupy one sublattice while other atoms occupy another sublattice. If there are more than two sublattices, the compound or solution shows a long-range ordering structure. For instance, in the three-sublattice model of (A,B,C,…)3(X,Y,Z,…)2(P,Q,R,…), the first sublattice is occupied by A/B/C, while the second sublattice is occupied by X/Y/Z and the third sublattice is occupied by P/Q/R. One of the species may also be found in more than one sublattice. The site fraction term is used for thermodynamic calculations. The site fraction of ith species on the first sublattice (yi´) is calculated by the ratio of moles amount of i on the first sublattice to the total mole amount of all species on the first sublattice, eq. (32). The site fractions yi´´ and yi´´´ of ith species on the second and third sublattices are also found similarly. The molar Gibbs energy change of mixing can be calculated by eq. (33). In eq. (33), ∆G°i represents the Gibbs free energy change of an end-member. If there are three elements on each of the three sublattices, there are 27 end-members in the solution. The first set of square brackets in eq. (33) is named as the mechanical mixing energy. The second set of the square bracket is related to the configurational entropy terms. While the third set of the square bracket is related to excess Gibbs free energy terms [17].

Modeling Short-Range Ordering

The graphs of the thermodynamic variables (the molar enthalpy or entropy changes of mixing, etc.) in a binary system can be obtained in different shapes, like v-shape or m-shape. These shapes result from the short-range ordered (SRO) solutions. The minimum ΔHM and ΔSM values are obtained near the compositions of the short-range ordered phases. This kind of shaped graph cannot be obtained by using a random-mixing model. The molecular models (or associated models) are commonly used for SRO. The molecular models suggest that there is a reaction realized between the constituents of the system inside the liquid form and a molecule