1. Introduction

The study of phase transformations is one of the most important problems in the physics of metals [1–3]. Phase transformations are divided into diffusion and nondiffusion [1]. If the kinetics of phase transformation in steels and cast irons is determined by the diffusion of carbon, this allows them to be attributed to conversions controlled by diffusion [1–4]. Such transformations in iron-carbon alloys include pearlitic transformation of austenite, and transformations occurring during tempering, graphitization of undoped cementite, separation of carbides in alloyed steels, and others [4–6].

When the rate of transformation of austenite is determined by the rate at which the interface separates, differing only in its crystalline structure, the transformation is called nondiffusion [1]. Kinetically, the normal polymorphic and martensitic transformations of austenite are distinguished. When the temperature of the normal transformation decreases, its velocity first increases and then decreases. The kinetics of the martensitic transformation is characterized by a very high rate of growth of individual crystals and the maximum space velocity at the initial moment of transformation under isothermal conditions.

In addition to martensite, at least two other structural components are known, which are formed with a shear ("martensitic") morphology of crystal formation ferrite side-plates and acicular ferrite. They can also be attributed, with some simplifying assumptions, to the products of the nondiffusion transformation of austenite. In addition, in some alloys martensitic and normal transformations occur at the same temperature [1]. The consistent theory of nondiffusion transformations should explain this phenomenon. Thus, the theoretical description of the processes of phase transformations in iron-carbon alloys is a complex and urgent task of modern metal physics.

Nonequilibrium thermodynamics provides the necessary apparatus for analyzing the processes of phase transformations in iron-carbon alloys [7–9]. In the general case, the thermodynamic equations of motion have the form [7]:

$$J\_i = \sum\_{\mathbf{x}=1}^{N} L\_{ik} X\_k(\mathbf{i} = \mathbf{1}, \dots, \mathbf{N}), \tag{1}$$

The main question that must be solved when using the Onsager Eqs. (1)–(3) is

In [5], for the first time on the basis of a special variational procedure, an expression for the cross coefficients in the Onsager equations was proposed in the

Using the Principles of Nonequilibrium Thermodynamics for the Analysis of Phase…

<sup>L</sup><sup>21</sup> <sup>¼</sup> <sup>L</sup><sup>12</sup> ¼ � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

As shown in [6, 11], in the complex process with two flows, an increase in the potential of one of the charges is observed, that is, one process is "leading," and the other is "driven." The "driven" process in itself, i.e., in isolation from the "lead," is not possible, since thermodynamically not beneficial. In the system of Eqs. (2) and (3), the thermodynamic force (�ΔμFe) is negative and inhibits the process as a whole, the diffusion of iron is a forced process, and the leading one is the diffusion of carbon. Thus, the graphitization process must be accompanied by a very intensive transfer of a solid solution (mainly iron), which makes it possible for the phase with a low-density graphite to grow in it. The authors of [6, 11] assumed that the factor contributing to graphitization is the pressure that arises in the austenite matrix under the action of graphite inclusions that expand it. However, in [12], considering the mechanism of graphitization of cast irons during thermocyclic treatment, K.P. Bunin with AA. Baranov came to the conclusion that the absolute value of the contact pressures is an order of magnitude less than the necessary for the dislocation creep mechanism under the influence of contact pressure. Since graphite films in pores cannot possess super strong properties, the evacuation of matrix atoms is

and the sign–before the root is chosen on the basis that the observed flux of iron

In [5], using nonequilibrium thermodynamic methods, it was shown that under the conditions of the system's striving for dynamic equilibrium, the concentration of vacancies in graphite inclusion becomes less than the vacancy concentration at the γ-phase-graphite boundary. This can occur as a result of approaching the γ-phase boundary—graphite of austenitic vacancies. In this case, the thermodynamic force (�Δμ0v) prevents the graphitization, and the reduced graphitization

Thus, the goal of this paper is to show how the methods of nonequilibrium thermodynamics can be used fruitfully to solve the theoretical problems of metal physics, namely, the analysis of phase transformations. Let us further consider the application of the principles of nonequilibrium thermodynamics to the analysis of

Consider the process of separation of carbides in a low-carbon steel system of iron-carbon-chromium with 0.15% carbon and about 5% chromium at 600°C. In this model system, there are two phases—the doped α-phase (F) and carbides (K), in which carbon, iron, chromium, and vacancies flows (Figure 1). As charges, we will use four quantities—the concentrations of carbon, iron, chromium, and vacancies. The flow of vacancies in the carbide phase will be assumed to be equal to the

In the absence of a change in the volume of the system, for flows in the doped α

force (�Δμ\*С) decreases to zero and can even take a negative value.

2. Formation of carbides in chrome steel during tempering

specific cases of phase transformations in iron-carbon alloys.

<sup>L</sup><sup>11</sup> � <sup>L</sup><sup>22</sup> <sup>p</sup> , (4)

the values of the cross coefficients.

DOI: http://dx.doi.org/10.5772/intechopen.83657

with respect to the flow of carbon had a negative sign.

apparently carried out by another mechanism.

flow of vacancies in the ferrite.

phase, condition [13] is fulfilled:

105

form:

where Ji are flows, Xk are the thermodynamic forces, Lik = Lki are the Onsager kinetic coefficients [9], and i, k are the charge numbers (transfer substrates).

The main driving forces of phase transformations in nonequilibrium thermodynamics are gradients of the chemical potentials of their components [6–9]. When discontinuous systems are considered, the finite differences of chemical potentials (�Δμi,) as the transition from a metastable state to a stable state are used as thermodynamic forces [10, 11]. Equations of nonequilibrium thermodynamics were first used in the physics of metals to describe the process of graphitization of nonalloyed iron-carbon alloys [6, 11].

As is known, unalloyed cementite in iron-carbon alloys at normal pressure is a metastable phase, its activity in phases with it in equilibrium exceeds the solubility of graphite, a stable phase [11]. Therefore, at a sufficiently high temperature, graphitization of such alloys takes place, that is, phase transition from metastable to stable equilibrium. Despite the seeming simplicity of this process, its theoretical description is a complex task.

If two values are used as charges of the graphitization process-carbon and iron concentrations, then, according to (1), the equations of motion take the form:

$$J\_1 = L\_{11}X\_1 + L\_{12}X\_2 \tag{2}$$

$$J\_2 = L\_{21}X\_1 + L\_{22}X\_2 \tag{3}$$

where J1 is the carbon flow characterizing the rate of the graphitization process, J2 is the flow of iron, and X1 = (�ΔμFe) and X2 = (�ΔμC) are the thermodynamic forces of iron and carbon. The potential drop has a "þ" sign as it increases, and the flow is directed toward a decrease in the potential, so the expressions for the forces contain the sign "�."

Using the Principles of Nonequilibrium Thermodynamics for the Analysis of Phase… DOI: http://dx.doi.org/10.5772/intechopen.83657

The main question that must be solved when using the Onsager Eqs. (1)–(3) is the values of the cross coefficients.

In [5], for the first time on the basis of a special variational procedure, an expression for the cross coefficients in the Onsager equations was proposed in the form:

$$L\_{21} = L\_{12} = -\sqrt{L\_{11} \times L\_{22}} \tag{4}$$

and the sign–before the root is chosen on the basis that the observed flux of iron with respect to the flow of carbon had a negative sign.

As shown in [6, 11], in the complex process with two flows, an increase in the potential of one of the charges is observed, that is, one process is "leading," and the other is "driven." The "driven" process in itself, i.e., in isolation from the "lead," is not possible, since thermodynamically not beneficial. In the system of Eqs. (2) and (3), the thermodynamic force (�ΔμFe) is negative and inhibits the process as a whole, the diffusion of iron is a forced process, and the leading one is the diffusion of carbon.

Thus, the graphitization process must be accompanied by a very intensive transfer of a solid solution (mainly iron), which makes it possible for the phase with a low-density graphite to grow in it. The authors of [6, 11] assumed that the factor contributing to graphitization is the pressure that arises in the austenite matrix under the action of graphite inclusions that expand it. However, in [12], considering the mechanism of graphitization of cast irons during thermocyclic treatment, K.P. Bunin with AA. Baranov came to the conclusion that the absolute value of the contact pressures is an order of magnitude less than the necessary for the dislocation creep mechanism under the influence of contact pressure. Since graphite films in pores cannot possess super strong properties, the evacuation of matrix atoms is apparently carried out by another mechanism.

In [5], using nonequilibrium thermodynamic methods, it was shown that under the conditions of the system's striving for dynamic equilibrium, the concentration of vacancies in graphite inclusion becomes less than the vacancy concentration at the γ-phase-graphite boundary. This can occur as a result of approaching the γ-phase boundary—graphite of austenitic vacancies. In this case, the thermodynamic force (�Δμ0v) prevents the graphitization, and the reduced graphitization force (�Δμ\*С) decreases to zero and can even take a negative value.

Thus, the goal of this paper is to show how the methods of nonequilibrium thermodynamics can be used fruitfully to solve the theoretical problems of metal physics, namely, the analysis of phase transformations. Let us further consider the application of the principles of nonequilibrium thermodynamics to the analysis of specific cases of phase transformations in iron-carbon alloys.
