Undercooled 7 phase

It should be mentioned that for 80CB the high-pressure smectic A and the reentrant nematic are only observed as supercooled, metastable phases that are not always found in a high-pressure experiment. Metastability has often been noticed in the study of liquid crystals. The retarded onset of a phase transition is frequently accompanied by a so-called exothermic anomaly in DTA experiments, where the undercooled phase transforms on reheating. In some cases monotropic meso-phases have been found, which are only observed on cooling, for example, smectic phases for 7PCH and 5CCH (cf. Table II). ... 

In this section we discuss the basic mechanisms of pattern formation in growth processes under the influence of a diffusion field. For simphcity we consider the sohdification of a pure material from the undercooled melt, where the latent heat L is emitted from the solidification front. Since heat diffusion is a slow and rate-limiting process, we may assume that the interface kinetics is fast enough to achieve local equihbrium at the phase boundary. Strictly speaking, we assume an infinitely fast kinetic coefficient. 

Here U = T — T )Cp/L is the appropriately rescaled temperature field T measured from the imposed temperature of the undercooled melt far away from the interface. The indices L and 5 refer to the liquid and solid, respectively, and the specific heat Cp and the thermal diffusion constant D are considered to be the same in both phases. L is the latent heat, and n is the normal to the interface. In terms of these parameters,... 

Our main interest here is concerned with patterns which can grow at constant speed even at low undercoolings A < 1, because if they exist they will dominate the system s behavior. A two-phase structure must then exist behind the growth front, filling the space uniformly on sufficiently... 

The aim is to predict, for given undercooling A and anisotropy e, the type of the two-phase structure and its characteristic length scales and velocity that is, to calculate the functions/ and v in the relation (80). The results will be summarized in the morphology diagram shown in Fig. 6. As it turns out. 

In the perspective discussed in the present contribution, bundle formation occurs within the amorphous phase and in undercooled polymer solutions. It does not imply necessarily a phase separation process, which, however, may occur by bundle aggregation, typically at large undercoolings [mode (ii)]. In this case kinetic parameters relating to chain entanglements and to the viscous drag assume a paramount importance. Here again, molecular dynamics simulations can be expected to provide important parameters for theoretical developments in turn these could orient new simulations in a fruitful mutual interaction. 

However, the situation is different if one considers the total transformation, including the solidus and peritectic type reactions where substantial solid state difflision is needed to obtain complete equilibrium. Unless very slow cooling rates are used, or some further control mechanism utilised in the experiment, it is quite common to observe significant undercooling below the equilibrium temperature of transformation. The following sections will briefly describe determinations of phase diagrams where non-isothermal techniques have been successfully used, and possible problems associated with non-equilibrium effects will be discussed. 

P and a represent, respectively, the undercooled liquid, the b.c.c. solid solution and the amorphous phase. ( ) are results from enthalpy of crystallisation experiments. Horizontal bars represent amorphous phase (I) interdifliision reaction and (2) by laser-quenching. 

As had been found in the glass-forming systems, the predicted undercoolings for compounds could vary markedly both between various types alloy systems and between various competing phases in the same alloy system. 

Fig. 3. Phase diagram of a portion of ihe Sitb-AbO% system, showing regions of phase separation of undercooled melts. The projected composition of Class-F fly ash glasses lies in the range of 10-4051 mol /t AI,Ot. Adapted from Roth et al. (1987).

Vapor-phase deposition of the sputtered or evaporated layer-forming material avoids the undercooling problems associated with liquid phase epitaxy, but it coats everything in the vaporization chamber unselectively. Sputtering is usually done by forming a plasma (ionized gas) in an electrical discharge in the vapor at low pressure. 

In Figure 1 the volume V, or the enthalpy H, are schematically plotted vs. temperature. By lowering the temperature of the liquid phase (upper right hand side of the figure), both decrease steadily. If crystallization occurs at the temperature Tat volume and enthalpy decrease abruptly. The state of an undercooled liquid can be reached if crystallization is somehow suppressed at Tat as shown in the upper curve of Figure 1. Upon further cooling, this curve shows an inflection at Tg, indicating a smaller temperature coefficient of V and H. 

Under ordinary laboratory conditions (at lower temperatures than shown in Fig. 7.5), it is seen that only the red a-sulfur form is stable. The yellow /3-sulfur needles are the most stable phase only in a narrow temperature range around 96-120°C, but they persist as a supercooled metastable phase well below this range (surviving, for example, on a stock-room shelf for indefinite periods). Given a sample of yellow /3-sulfur, it is easy to detect the melting point near 120°C, but is far from easy to detect the enantiomorphic a/13 solid-solid conversion near 96°C, unless a nucleating crystallite or catalyst is introduced. Once produced, the /3-phase tends to persist as a supercooled (undercooled) metastable extension... 

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