An important section of thermodynamics is the study of transformations between different phases of a substance, since these processes occur in practice and are of fundamental importance for predicting the behavior of a system under certain conditions. These transformations are called phase transitions, which the article is devoted to.
The concept of phase and system component
Before proceeding to the consideration of phase transitions in physics, the concept of the phase itself should be defined. As you know from the course of general physics, there are three states of matter: gaseous, solid and liquid. In a special section of science - in thermodynamics - laws are formulated for the phases of matter, and not for their state of aggregation. Under the phase is understood a certain volume of matter, which has a homogeneous structure, is characterized by specific physicochemical properties and is separated from the rest of the matter by boundaries, which are called interfacial.
Thus, the concept of “phase” carries much more practically significant information about the properties of matter than its state of aggregation. For example, the solid state of a metal such as iron can be in the form of the following phases: low-temperature magnetic body-centered cubic (bcc), low-temperature non-magnetic bcc, face-centered cubic (fcc) and high-temperature non-magnetic bcc.
In addition to the concept of “phase”, the term “components” is also used in the laws of thermodynamics, which means the number of chemical elements that make up a particular system. This means that the phase can be either monocomponent (1 chemical element) or multicomponent (several chemical elements).
Gibbs theorem and the equilibrium between the phases of the system
To understand the phase transitions, it is necessary to know the equilibrium conditions between them. These conditions can be mathematically obtained by solving the system of Gibbs equations for each of them, assuming that the equilibrium state is reached when the total Gibbs energy of the system, isolated from the external influence, ceases to change.
As a result of solving the indicated system of equations, conditions are obtained for the existence of equilibrium between several phases: an isolated system will cease to evolve only when the pressures, chemical potentials of each component and temperature in all phases are equal to each other.
Gibbs phase rule for equilibrium
A system consisting of several phases and components can be in equilibrium not only under certain conditions, for example, at a specific temperature and pressure. Some variables in the Gibbs theorem for equilibrium can be changed, preserving both the number of phases and the number of components in this equilibrium. The number of variables that can be changed without disturbing the equilibrium in the system is called the number of freedoms of this system.
The number of freedoms l of a system consisting of f phases and k components is determined uniquely from the Gibbs phase rule. This rule is mathematically written like this: l + f = k + 2. How to work with this rule? Very simple. For example, it is known that the system consists of f = 3 equilibrium phases. What is the minimum number of components such a system can contain? The question can be answered by reasoning as follows: in the case of equilibrium, the most stringent conditions exist when it is realized only at certain indicators, that is, a change in any thermodynamic parameter will lead to imbalance. This means that the number of freedoms is l = 0. Substituting the known values of l and f, we obtain k = 1, i.e., a system in which three phases are in equilibrium can consist of one component. A striking example is the triple point of water, when ice, liquid water and steam exist in equilibrium at specific values of temperature and pressure.
Classification of phase transformations
If we begin to change some thermodynamic parameters in a system in equilibrium , then we can observe how one phase will disappear and another will appear. A simple example of this process is the melting of ice when it is heated.
Given that the Gibbs equation depends on only two variables (pressure and temperature), and the phase transition involves a change in these variables, then the mathematical transformation between the phases can be described by differentiating the Gibbs energy with respect to its variables. It was this approach that the Austrian physicist Paul Ehrenfest used in 1933, when he compiled a classification of all known thermodynamic processes that occur with a change in phase equilibrium.
From the fundamentals of thermodynamics it follows that the first derivative of Gibbs energy with respect to temperature is equal to the change in the entropy of the system. The pressure derivative of Gibbs energy is equal to the change in volume. If the entropy or volume undergoes a break when changing phases in the system, that is, they change sharply, then they speak of a first-order phase transition.
Further, the second Gibbs energy derivatives with respect to temperature and pressure are the specific heat and volume expansion coefficient, respectively. If the transformation between the phases is accompanied by a discontinuity in the values of the indicated physical quantities, then they speak of a second-order phase transition.
Examples of transformations between phases
There are a huge number of different transitions in nature. In the framework of this classification, striking examples of first-order transitions are the processes of metal melting or condensation of water vapor from air when a volume jump in the system occurs.
If we talk about transitions of the second kind, then vivid examples are the transformation of iron from magnetic to paramagnetic state at a temperature of 768 ºC or the transformation of a metal conductor into a superconducting state at temperatures close to absolute zero.
Equations that describe first-order transitions
In practice, it is often necessary to know how temperature, pressure and absorbed (released) energy in a system change when phase transformations occur in it. Two important equations are used for this purpose. They are obtained on the basis of knowledge of the basics of thermodynamics:
- The Clapeyron formula, which establishes the relationship between pressure and temperature during transformations between different phases.
- Clausius formula, which connects the absorbed (released) energy and temperature of the system during the transformation.
The use of both equations consists not only in obtaining quantitative dependences of physical quantities, but also in determining the sign of the slope of the equilibrium curves in phase diagrams.
The equation for the description of transitions of the second kind
Phase transitions of the 1st and 2nd kind are described by different equations, since the application of the Clapeyron and Clausius equations for transitions of the second kind leads to mathematical uncertainty.
To describe the latter, the Ehrenfest equations are used, which establish the relationship between changes in pressure and temperature through knowledge of changes in heat capacity and volume expansion coefficient during the transformation process. The Ehrenfest equations are used to describe the conductor – superconductor transitions in the absence of a magnetic field.
The importance of phase diagrams
Phase diagrams are graphical representations of areas in which the corresponding phases exist in equilibrium. These areas are separated by lines of equilibrium between the phases. Often used phase diagrams on the axes PT (pressure-temperature), TV (temperature-volume) and PV (pressure-volume).
The importance of phase diagrams is that they allow you to predict which phase the system will be in when the external conditions change accordingly. This information is used in the heat treatment of various materials in order to obtain structures with desired properties.