A thermodynamic model of hysteresis in phase transitions and its application to rare earth oxide systems

Abstract

A thermodynamic model of hysteresis in phase reactions based on regular solution theory is developed by invoking metastabilities. The effect of enthalpy and entropy change, pressure, temperature, and interaction energy on the hysteresis curve term is explored. The influence of a variation of the interaction term with temperature and composition is also studied. Observed hysteresis for the phase reactions Tb,Ol,P712Tb,03 + 3/40, and Pr9016 P 9/7Pr,012 + 2170, is discussed and the theory is applied to each case. The experimental details of data acquisition and the observed hysteresis in the praseodymium oxide reaction are given.

Effect of the specific surface area on thermodynamic and kinetic properties of nanoparticle anatase TiO2 in lithium-ion batteries

“…The thermodynamic equilibrium potential of Li-ion (de-)insertion, E t , is defined as the midpoint of the distance between thermodynamic potentials of the plateau for Li-ion (de-)insertion as derived from the relaxation potential curves. This is based on Gibbs' theory of metastable phases, which predicts that the equilibrium potential should lie in between the two metastable potential lines [35]. In literature, the distance between the equilibrium potential and the metastable potential is named hysteresis; however, it could be better defined as a metastable overpotential, which is indicated with the symbol h h .…”

Van der Waals-like behaviour of charged black holes and hysteresis in the dual QFTs

“…A quite general thermodynamical explanation of hysteresis associated with phase transitions has been given and is related to meta-stabilities [32,33]. Whenever we have at least two stable states -say A and B, respectively on the left of the maximum and on the right of the minimum of fig.…”

Hysteresis in $$\eta /s$$ η / s for QFTs dual to spherical black holes

“…When the system evolves from large (small) BHs to small (large) BHs a potential barrier prevents the evolution of the system from occurring as an equilibrium path between the two stable states [78]. Equilibrium will be reached passing through a meta-stable region [77] and a path-dependence ofη/s is generated. The presence of these local extrema determines the patterns of signs of the BH specific heat and free energy, hence the local thermodynamical stability [14,63].…”

“…(20) or, equivalently, to the presence of two stable states (small and large BHs) connected by a meta-stable region (intermediate BHs). This phase portrait has been considered as a general explanation of hysteretic behavior for some variables of the system [77]. In particular, when the system evolves from high (low) to lower (higher) temperatures, a potential barrier prevents the evolution of the system from occurring as an equilibrium path between the two stable states [78].…”