First-order phase transition definition

The martensite - austenite transition temperatures we find are for all systems in accordance with the previously published ones . Some minor deviations can be attributed to the fact that we are simulating an overheated first order phase transition. Therefore, for our limited system sizes, one cannot expect a definite transition temperature. 

The problematic nature of the melting transition can be illustrated by comparison with other well-known first-order phase transitions, for instance the normal metal-(low T ) superconductor transition. The normal metal-superconductor and melting transitions have similar symptomatic definitions, the former being a loss of resistance to current flow, and the latter being a loss of resistance to shear. However, superconductivity can also be neatly described as a phonon-mediated (Cooper) pairing of electrons and condensation of Cooper pairs into a coherent ground state wave function. This mechanistic description of the normal metal-super-conductor transition has required considerable theoretical effort for its development, but nevertheless boils down to a simple statement, indicat-... 

As a final point, one must remember that first-order phase transitions are based on equilibrium and require a sharp transition at the intersection of the free enthalpy curves as seen in Figs. 2.84-88. As indicated in Fig. 2.120, the observed broadness comes mainly from a distribution of areas of different size and perfection causing the distributions of subsystems in Fig. 6.3 (for the definition of subsystems see Fig. 2.80). Combining the different types of molecules, phases, and sizes with the range of metastable phase structures yields an enormous number of materials that must be explored to find the perfect match for the application on hand. 

Here are more rigorous definitions if the first partiaJ derivatives of the thermodynamic potentials G and F with respect to their natural variables have breaks during transition, it is called a first-order phase transition. If the mentioned derivatives remain continuous but some higher ones have their breaks (in particular, become infinite), we speak of high-... 

In a first order phase transition, thermodynamic functions by definition discon-tinuously change as one cools the system along a path crossing the equilibrium coexistence line (Fig. 5a, path j8). In a rea/experiment, however, this discontinuous change may not occur at the coexistence line because a substance can remain in a supercooled metastable phase until a limit of stability (a spinodal) is reached [2] (Fig. 5b, path fi). 

Polymer crystallization and melting are typically first-order phase transitions between the amorphous phase and the crystalline phase. When these two phases are in thermodynamic equilibrium, two phase transitions are thermodynamically reversible under a certain temperature. This temperature is referred to the equilibrium melting point of polymer crystallization. The free energy changes of amorphous phase and crystalline phase under various temperatures are depicted in Fig. 4.1, illustrating the definition of the equilibrium melting point 7. ... 

Order of the Paramagnetic-Antiferromagnetic Transition. A second-order transition is indicated by various studies with neutrons, Ott, Kjems [14], and the behavior of thermal expansion and heat capacity around the N6el temperature [5].The temperature dependence of critical scattering definitely excludes the existence of a smeared-out first-order phase transition [14]. How-... 

What is meant by "soft condensed matter " In the context of this NATO Advanced Study Institute, soft systems are those where the relevant interactions are weak and thermal fluctuations play an important role. However, this is not a sufficiently sharp definition because all materials that have higher order or weakly first order phase transitions, e.g, magnetic materials, superconductors, etc., have this property. I believe that "softness," in addition, implies a relatively high bulk or osmotic compressibility. For a system with a transition temperature, Tc, the elastic modulus, G, scales as... 

Another type of transition is the second-order phase transition in which the first derivative of the chemical potential is continuous while the second derivative is not. This means that enthalpy, volume, and entropy vary continuously with temperature through a second-order phase transition temperature. This behavior is qualitatively different from that of a first-order phase transition, as illustrated in Figure 4.5. Whereas first-order phase transitions occur at a definite temperature for a given pressure, and with separation of the phases, second-order transitions do not exhibit a separation of phases and occur over a range of temperatures. The transition from superfluid helium to normal liquid helium and the transition from being a superconducting metal to being an ordinary conductor are examples of second-order transitions. 

Point 7 has very special properties. It occurs at random close-packing density and provides a definition of it. Point / is an isostatic point, where the number of particle contacts equals the number of force balance equations to describe them. As a result, it is a purely geometrical point the properties of the state at point / are independent of potential. Also, point / appears to be a zero-temperature mixed phase transition, with a discontinuity in the number of contacts, characteristic of first-order phase transitions, and diverging length scales, characteristic of second-order phase transitions. 

Both spin-crossover transitions (HS < LS, FO LS) are first order accompanied by definite jumps of populations, while the cooperative Jahn-Teller transition (HS FO) is weak first-order (very close to a second-order transition). It suggests a possibility of observation of hidden cooperative Jahn-Teller transition (the broken line in Fig. 7) between the metastable HS and FO phases, if the HS phase could be supercooled enough below the spin-crossover transition temperature Tc by a rapid cooling. 

Given that (see Fig. 9.8) at the glass transition temperature, the specific volume Vs and entropy S are continuous, whereas the thermal expansivity a and heat capacity Cp are discontinuous, at first glance it is not unreasonable to characterize the transformation occurring at Tg as a second-order phase transformation. After all, recall that, by definition, second-order phase transitions require that the properties that depend on the first derivative of the free energy G such as... 

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

The transitions between the bottom five phases of Fig. 2 may occur close to equilibrium and can be described as thermodynamic first order transitions (Ehrenfest definition 17)). The transitions to and from the glassy states are limited to the corresponding pairs of mobile and solid phases. In a given time frame, they approach a second order transition (no heat or entropy of transition, but a jump in heat capacity, see Fig. 1). 

However, it is useful, to provide a thermodynamic definition of a first-order transition. Specifically, it is one in which there is a discontinuity in a first derivative of the Gibbs free energy. The advantage of this definition is the guidance it provides for the experimental study of phase transitions. A useful expression for the free energy in this regard is... 

The Statistical Rate Theory (SRT) is based on considering the quantum-mechanical transition probability in an isolated many particle system. Assuming that the transport of molecules between the phases at the thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between the two phases 1 and 2 , R 2, was developed by using the first-order perturbation analysis of the Schrodinger equation and the Boltzmann definition of entropy. 

Generally, a tricritical point is defined as the point, where three phases become identical. Alternatively a tricritical point can be defined as the point where a second order A-line of an order transition becomes first order or else as the point, where a A-line cuts a coexistence curve at its critical point [4, 5], The last definition is relevant for the ionic fluids. 

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