The interactions between thermodynamic anomalies

Abstract

The origin of and interactions between key thermodynamic anomalies are derived and analyzed, as are the interactions with the stability (or cavitation) limits. The conditions for interaction are derived from the underlying thermodynamic relations rather than using the morecommonly applied Taylor expansion method. As a result, we derive a general set of equations that govern the interactions between different lines of thermodynamic anomalies using standard manipulation of thermodynamic equations. The validity of the derivations is investigated by comparing them to numerical simulation data and previous Taylor expansion-based results. Simulations are performed using a modified Stillinger-Weber potential in which the balance of the two-and three-body interactions is varied and which serves to highlight the relationships between the various anomalies. The deeply supercooled regime is explored by employing replica exchange methods. The behavior of the anomalies is considered in terms of previously constructed thermodynamic "scenarios." Based on the newly uncovered interaction schemes, we propose a classification strategy for the thermodynamic anomalies (as first-or second-order) which could be extended to additional related anomalies.

Thermodynamic anomalies in silicon and the relationship to the phase diagram

“…The panel also highlights the region of the phase space for which crystallisation appears unavoidable (region labelled 'crys.'). In panels (a) and (c) the dashed lines show extrapolations of the observed loci to regions of phase space in which they are not resolved in our simulations though are consistent with thermodynamic analysis [29]. Panel (d) shows the set of anomalies from panel (a) but in the VT projection.…”

“…As the TMD line becomes re-entrant it collides with the stability limit as shown, re-emerging as the TminD line at lower temperature which then extends from negative to positive pressure. The collision of both the TMD and TminD loci with the stability limit occur at zero gradient for the latter as required [29], with the collisions at {p, T} = {−4.2 GPa, 1780 K} for the TMD and {p, T} = {−3.5 GPa, 1130 K} for the TminD. The shape of the stability limit shows a local maximum and minimum as a result of the intersection with the set of density anomaly loci.…”

“…Figure 1 shows the complete set of anomalies studied along with the stability limit for the potential parameter λ = 21 (most appropriate to model liquid silicon) and acts to highlight the known relationships between them [29,31,32,48] and which we shall elaborate on below. Figure 1(a) shows the complete set of anomalies (and related properties) obtained here.…”

“…In one case work has focussed on mapping how the anomalies shift in phase space as a potential model is systematically modified [30]. In the second case the mathematical constraints, which govern how these anomalies may intersect and interact with each other and stability limits, have been studied [29]. The latter builds on the previous work which linked the compressibility and density anomaly loci [11] and the heat capacity and density analogues [29,31,32].…”

From Critical Point to Critical Point: The Two-States Model Describes Liquid Water Self-Diffusion from 623 to 126 K

“…For water, it holds only for K, while, below this temperature, entropy and volume fluctuations are negatively correlated: the coefficient of thermal expansion becomes negative so that a volume increase provokes an entropy decrease. In addition, entropy and volume fluctuations show a net increase when cooling liquid water below T* ≃ 320 K down to the supercooled regime [ 10 , 11 , 12 ]. This temperature, which is only few degrees above the body temperature of mammals, coincides with the onset of the protein thermal unfolding [ 13 ].…”