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Phase equilibria: non-reactive systems
Published in W. John Rankin, Chemical Thermodynamics, 2019
The relationship between the Gibbs energy of mixing and a binary temperature−composition diagram is shown schematically in Figure 13.15 for a system with a miscibility gap. The ΔmixGmcurves are shown for temperatures T1 to T6, where the increasing numbers designate increasing temperatures. The points where the common tangents touch the curves give the compositions of the equilibrium phase(s) at the corresponding temperatures. The curve joining these points defines the phase boundary of the miscibility gap as a function of temperature. Temperature T5 is the critical temperature of the system. At temperatures greater than T5 there is complete miscibility, and the ΔmixGm curve has the familiar shape of a mixing curve. The variation of the activity of A and B at T4 is shown in the bottom graph. For both components the standard state is the pure liquid at 1 bar and temperature T4. The activities of A and B are constant across the miscibility gap because the chemical potentials of A and B are constant.
Systems Containing Three Phases
Published in D. R. F. West, N. Saunders, Ternary Phase Diagrams in Materials Science, 2020
The concept of a miscibility gap may be illustrated by reference to the portion of binary diagram shown in Figure 4.21 ; there is partial solubility in the liquid state, and the region in which two liquidus co-exist is termed the miscibility gap. In the case shown, as the temperature increases the tie-lines spanning the miscibility gap become shorter, until, at the temperature of the critical point, c, the tie-line has zero length and the gap closes; above this temperature there is complete liquid solubility.
Phase transitions and phase coexistence: equilibrium systems versus externally driven or active systems - Some perspectives
Published in Soft Materials, 2021
When, for a system in thermal equilibrium, one has a phase diagram of the type in Fig 2, a state within the miscibility gap means two-phase coexistence, with both phases having then the same temperature and pressure . It is already a nontrivial issue to give these quantities a precise and unique meaning (recall that also for the Rayleigh-Bénard problem), [66] we had to deal with a space-and-time-dependent temperature field, but due to the macroscopic character of the problem, the formulation of Equations 5,6 rested on a local equilibrium assumption, so there was no problem to define what the temperature field meant). For the mesoscopic active particles of interest in the present section, we have a well-defined temperature for the background fluid of the colloid suspension, responsible for the noise terms in the Brownian motion (cf. Equation 10), but this temperature has nothing to do with the effective temperature related to the average translational kinetic energy of the active particles, ( denotes the mass of the active particles). Now it turns out that for the model defined by Equations 9 10 indeed is constant in the steady states of the system, but this is not the case for a slightly different model, [17] where one considers underdamped rather than overdamped Brownian motion, where an acceleration term is added to the friction term in Equation 9, and also the moment of inertia I needs to be accounted for orientational relaxation.[17] In this case, particles in the gas phase are typically much faster than in the dense phase. It has been shown that the coexistence of phases is possible which have different kinetic temperatures!
Magnetic-field-induced phase separation via spinodal decomposition in epitaxial manganese ferrite thin films
Published in Science and Technology of Advanced Materials, 2018
Nipa Debnath, Takahiko Kawaguchi, Harinarayan Das, Shogo Suzuki, Wataru Kumasaka, Naonori Sakamoto, Kazuo Shinozaki, Hisao Suzuki, Naoki Wakiya
Figure 7(a) shows the out-of-plane lattice parameters of Mn-rich and Fe-rich phases in phase-separated Mn ferrite of different average film composition deposited under 2000 G magnetic field at 500–700 °C growth temperature. The out-of-plane lattice parameters of Mn-rich and Fe-rich phases are calculated from the corresponding 2θ values of the Bragg peaks in XRD patterns. We have mentioned in Section 3.1 that the Mn-rich and Fe-rich phases should have larger and smaller lattice parameters, respectively. From Figure 7(a), it is also confirmed that the lattice parameter of Mn-rich phase is larger than that of Fe-rich phase in case of all phase-separated films of different composition. The lattice parameters of Mn-rich phase in all Mn ferrite films deposited at 700 °C are almost same. The 500 °C and 600 °C films have similar or smaller out-of-plane lattice parameters of Mn-rich phase. The lattice parameters of Fe-rich phase in all 700 °C thin films are also independent on average film composition. It is found that the out-of-plane lattice parameters of Fe-rich phase scatter a little at other growth temperatures in all phase-separated Mn ferrite films. Lattice distortions in the Fe-rich phase were confirmed by RSM images, and its in-plane lattice parameters approach those of MgO, leading to a close in-plane matching with the substrate. Hence, it can be claimed that whatever the average film composition is, the out-of-lattice parameters of Mn-rich phase in all phase-separated Mn ferrite films have almost same values indicated by the red dashed line in Figure 7(a). And the similar fact is also true for the lattice parameters for Fe-rich phase in Mn ferrite films indicated by the green dashed line in Figure 7(a). In addition, there is a significant difference between the composition (lattice parameters) of two phases in phase-separated Mn ferrite films. The miscibility gap in the phase diagram of any material system defines the composition range within which a homogeneous solid solution becomes unstable [2]. Presumably, the compositions of Mn-rich and Fe-rich phases in spinodally decomposed Mn ferrite films maintain a certain range. It can be qualitatively said that this range of composition of phase-separated Mn ferrite films can be defined as miscibility gap in MnFe2O4-Mn3O4 system.