(a) Crystal enthalpies for perfect crystals FCT, smectic B and Donev-1 at T = 0.1, (reduced units T = kT/∈0) compared with the enthalpies of the defect crystals obtained from freezing liquids at aspect ratios α = 1.1, 3.0, and 2.2, respectively, and then tuning α within the crystal state as described in text. Included for comparison are the enthalpies of glassy states obtained by HQ for all α values, and by SC for values in the glassforming range. Evidently, at α = 1.4, no crystal tested in this work has significantly lower enthalpy than the slow-cooled glass. (b) Fusion enthalpies of crystals of different aspect ratio α, in the G-B model. Note good agreement of extrapolation to α = 1, with value for pure LJ from Ref. 22 .
Melting points (in reduced units, T = kT/∈0, see text) observed during heating of the defect crystals, compared with ergodicity-breaking temperatures during slow cooling, identified in Figure 3 as Tg. 24 Note that Tm values assessed close to Tg by our method (or any other) will be falsely high 25 because the equalization of chemical potentials at the melting point depends on particles being able to rearrange in space to yield the equilibrium liquid phase (see text). Values at lower aspect ratios extrapolate to Ref. 22 value for pure LJ. The V-shaped addition, bridging FCT and smectic B cases with the lowest melting points, shows the liquidus temperatures for mixtures of these substances according to ideal mixing laws (see text). The inset shows the large difference that can arise between actual eutectic temperatures, and their ideal mixing values predicted from melting enthalpies, when the mixing is highly non-ideal as in the system Au-Si in which the first metallic glasses were made. With such non-ideal effects, the G-B mixture we discuss here could have an extrapolated eutectic far below its Tg, and arguably also below the Kauzmann temperature (where Sliquid = Scrystal). We will give new experimental data to illustrate these issues in the concluding remarks section of this paper.
(a) Enthalpies of the liquid and glassy states of the G-B model, for five values of aspect ratio α, spanning the pseudo-triple point in the temperature-potential phase diagram (Figure 2 ), and (b) the corresponding heat capacities. Enthalpies are shifted by 0.5 units from each other for clarity. The Cp plots are separated by 7 units from each other (low temperature value is the classical 3R in each case). The jump in Cp at Tg is 33% of the glass value in each of the glassformer cases shown (α = 1.4, 1.8, and 2.0). At α = 1.4 and 1.6 (not shown), the normal enthalpy hysteresis of glassformers disappears and the liquid behaves like the maximally fragile liquid case of Wang's hysteresis analysis. 29 The behavior at α = 1.2, where crystals nucleate at the Tg of the other liquids, is surprising (the subsequent crystal melting point accords with Fig. 2 values).
Glass transition temperatures and liquidus temperatures, where it was possible to measure them, in the systems ketoprofen + 4-picoline and ketoprofen + 2-picoline. The dashed blue lines correspond to the ideal melting point depression lines calculated using the measured enthalpies of fusion for the two components and describe the dilute solutions before non-ideal mixing effects begin to dominate. The red dashed lines through experimental points define the liquidus lines for ketoprofen and 4-picoline (4 pic), while that for 2-picoline (2 pic) is drawn to have, as expected, the same thermodynamics as for the measurable 4-picoline case (see text). The double arrow demarcates approximately the ideal glassformer domain, where the glass temperature is reached while the liquid is still thermodynamically stable.
Article metrics loading...
Full text loading...