In summary, the order of phase transitions can be determined by examining the continuity of the Gibbs function. If the Gibbs function is continuous but its slope is discontinuous, the transition is classified as first-order. If both the Gibbs function and its derivative are continuous but the second derivative is discontinuous, the phase change is considered second-order. The only known second-order transition is the conductor-superconductor transition in liquid He. Another type of transition is the 'lambda transition' where some thermodynamic properties diverge, leading to the development of renormalization and scaling concepts. The understanding of phase transitions has expanded in recent years, making some of the information in this discussion potentially outdated.
#1
j-lee00
95
0
How does one determine the order of phase transitions?
By the degree of continuity in the Gibbs function. If the Gibbs function is continuous, but its slope is discontinuous (say due to the latent heat of melting), the transition is first-order. If both the Gibbs function and it's derivative is continuous, but the second derivative is discontinuous, the phase change is a second-order. AFAIK, the conductor-superconductor transition in liquid He is the only known second-order transition, but I don't have any really up-to-date references.
There's also a 'lambda transition', in which some of the thermodynamics properties (specific heat, for example) diverges. The resolution of that led to renormalization and scaling concepts.
The concept of a phase transition has really expanded over the past 10 years or so- some of what I wrote may be out of date.
#3
sir-pinski
1,466
1
The order of phase transitions can be determined by examining the changes in the thermodynamic properties of a system during the transition. These properties include temperature, pressure, and volume.
There are three main types of phase transitions: first-order, second-order, and higher-order. First-order phase transitions involve a discontinuous change in the system's properties, such as a sudden change in volume or energy. Second-order phase transitions, on the other hand, involve a continuous change in the system's properties, without any sudden jumps.
To determine the order of a phase transition, one can look at the behavior of the system's properties near the transition point. For a first-order transition, there will be a sudden change in the system's properties at the transition point, while for a second-order transition, the properties will change continuously. Higher-order transitions involve more complex behavior, with multiple changes in the system's properties.
Another way to determine the order of a phase transition is by looking at the critical exponent of the system. This exponent describes how the system's properties change near the transition point. For first-order transitions, the critical exponent is usually non-zero, while for second-order transitions, it is zero.
In summary, the order of a phase transition can be determined by analyzing the behavior of the system's properties near the transition point and by calculating the critical exponent. Understanding the order of a phase transition is crucial in predicting the behavior of a system and can provide valuable insights into the underlying physical processes.