Temperature dependence transformation, phase coexistence

Simulations of octahedral molecular clusters at constant temperature show two kinds of structural phase changes, a high-temperature discontinuous transformation analogous to a first-order bulk phase transition, and a lower-temperature continuous transformation, analogous to a second-order bulk phase transition. The former shows a band of temperatures within which the two phases coexist and hysteresis is likely to appear in cooling and heating cycles Fig. 10 the latter shows no evidence of coexistence of two phases. The width of the coexistence band depends on cluster size an empirical relation for that dependence has been inferred from the simulations. 

Another important consideration is the metastability of many mineral phases in the near-surface environment. Kinetics of low-temperature mineral transformations and their dependence on the chemical conditions of coexisting fluids are not well known, despite the important influence these transformations may have on particle size, surface area, and the transport behavior of associated trace elements. Some of these issues can be addressed effectively using SR methods, but the long time scale of some such processes cannot be observed in typical experimental time scales. 

The temperature dependence of Tm obtained in these early experiments by both X-ray (open circles) and neutron diffraction (solid circles) is shown in fig. 6. It is clear that in the temperature range above 20 K the wave vector Vm determined by X-rays has preferred, commensurable values, whereas in the lower resolution neutron data there is a continuous variation of the wave vector with temperature. Other noteworthy features of the X-ray data include the appearance of an inflection point near tm = at around 70 K, thermal hysteresis below 50 K, and coexistence among phases with differing wave vectors. At the lowest temperatures, there is a first-order transition between two commensurable wave vectors, namely, = c and tm = gc, and there is an indication of a lock-in transformation at c. The inset in fig. 6 shows the variation of Tm during several cycles of the temperature between 25 K and 13K. The data suggest a clustering of the wave vectors around tjn = jfC and Tm =... 

Fredrickson and Binder [9] further improved this theory to describe the kinetics of the ordering process. Their concentration dependent free energy potential shows two side minima, which have the same depth as the middle one at the microphase separation transition temperature Tmst- Therefore, they presume a coexistence of the disordered and the lamellar phase at Tmot- As the temperature is further lowered, these side minima become dominant and the transition comes to completion. For a supercooled material, they expect after a completion time an Avrami-type ordering transformation with an exponent of 4 equivalent to spherically growing droplets of ordered material. This characteristic time corresponds to the time to form stable droplets of ordered material plus the time needed for the structures to grow to a size that they can be detected by the used technique. 

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