Some computational techniques 4. Ice does hence melt at constant temperature T < T0 when increasing the pressure P. This happens during skating on ice. At 205K the crys-tal lattice undergoes a discontinuous distor-tion represented in the ﬁgure by the param-eter . Consider two phases , α and β, in equilibrium. In real crystal structures, there is a wide class of phase transitions, known as order-disorder phase transitions, which are described in terms of scalar modes. Examples of rst-order and second-order phase transitions First-order magnetic and structural transition in SrFe2As2. The solid-liquid-gas phase transition of most substances is first order. conducting-superconducting transition in metals at low temperatures. Metastable states near first-order phase transitions stability 5. Notice the properties: • The second derivative of the thermodynamic potential is zero (the straight portion of A.V/) or inﬁnite (the cusp in G.P/). A second order transition (or continuous transition) will not give off any heat during the transition. When the first derivative of the free energy with respect to one of its dependent thermodynamic variables is discontinuous across a phase transition, this is an example of what is called a first order phase transition. 4.3. The melting curve of water has negative slope. Dynamics of first-order phase transitions 5.1. For example, the coexistence of water and vapor in a first order transition and the inability to distinguish gas and liquid beyond the critical point, which corresponds to 2nd order phase transition. For example, a liquid may be heated to a temperature above the boiling point or supercooled to below the freezing point. The existence of a metastable equilibrium region in the vicinity of a phase-transition curve is characteristic of a first-order phase transition. Most phase transitions involve changes in enthalpy and in volume. First-order and second-order phase transitions (II) G Ttrs ΔGtrs 0 Second-order phase transition T V Ttrs T S Ttrs T H Cp-S T G P V P G T -continuous (S and V do not jump at transition) Ttrs T Ttrs T Strs 0 Htrs 0 P P dT dH C e.g. Vtrs 0 P 2 T V T P G The existence of a metastable equilibrium region in the vicinity of a phase-transition curve is characteristic of a first-order phase transition. The phase transition we just described involves a change of colour of parts of the ﬁgure, and colour is a scalar variable, so we expect we will need scalar modes. ‘Essential’ singularity at a first-order phase transition 4.4. A transition in which the molar Gibbs energies or molar Helmholtz energies of the two phases (or chemical potentials of all components in the two phases) are equal at the transition temperature, but their first derivatives with respect to temperature and pressure (for example, specific @E02141@ of transition and @S05807@) are discontinuous at the transition point, as for two … Order of phase transitions First-order phase transitions. • As a function of the extensive variable Vthere is a region (between Vl and Vg)ofphase coexistence. This type of transition is a ﬁrst order phase transition. For example, a liquid may be heated to a temperature above the boiling point or supercooled to below the freezing point. These changes figure into the differences in the slope of the chemical potential curve on either side of the transition point. 6.2 First-order phase transition When water starts boiling, it undergoes a phase transition from a liquid to a gas phase. 64 CHAPTER 6. A first order transition (or discontinuous) will give off latent heat during the transition. In this case the phase diagram of the system becomes richer, with coexistence and critical lines that intersect in points called multicritical points; one of the most common examples of a multicritical point is the tricritical point, which divides a first-order transition line from a second-order one. PHASE TRANSITIONS Skating on ice. On the significance of the ‘spinodal curve’ and related limits of meta- 3. Decay of …