Solid Phase Transition

The CS pressures are close to the machine calculations in the fluid phase, and are bracketed by the pressures from the virial and compressibility equations using the PY approximation. Computer simulations show a fluid-solid phase transition tiiat is not reproduced by any of these equations of state. The theory has been extended to mixtures of hard spheres with additive diameters by Lebowitz [35], Lebowitz and Rowlinson [35], and Baxter [36]. 

Reiss H and Hammerich ADS 1986 Hard spheres scaled particle theory and exact relations on the existence and structure of the fluid/solid phase transition J. Phys. Chem. 90 6252... 

This section will describe the current status of research in two different aspects of nanocrystal phase behaviour melting and solid-solid phase transitions. In the case of melting, thennodynamic considerations of surface energies can explain the reduced melting point observed in many nanocrystals. Strictly thennodynamic models, however, are not adequate to describe solid-solid phase transitions in these materials. 

Unlike melting and the solid-solid phase transitions discussed in the next section, these phase changes are not reversible processes they occur because the crystal stmcture of the nanocrystal is metastable. For example, titania made in the nanophase always adopts the anatase stmcture. At higher temperatures the material spontaneously transfonns to the mtile bulk stable phase [211, 212 and 213]. The role of grain size in these metastable-stable transitions is not well established the issue is complicated by the fact that the transition is accompanied by grain growth which clouds the inteiyDretation of size-dependent data [214, 215 and 216]. In situ TEM studies, however, indicate that the surface chemistry of the nanocrystals play a cmcial role in the transition temperatures [217, 218]. 

The ability to control pressure in the laboratory environment is a powerful tool for investigating phase changes in materials. At high pressure, many solids will transfonn to denser crystal stmctures. The study of nanocrystals under high pressure, then, allows one to investigate the size dependence of the solid-solid phase transition pressures. Results from studies of both CdSe [219, 220, 221 and 222] and silicon nanocrystals [223] indicate that solid-solid phase transition pressures are elevated in smaller nanocrystals. 

More recently, studies of the hysteresis of these phase transitions have illuminated the importance of kinetic factors in solid-solid phase transitions [224]. The change between crystal stmctures does not occur at the same point when pressure is increasing, as when it is decreasing the difference between this up-stroke and down-stroke pressure... 

Tolbert S H and Aiivisatos A P 1994 Size dependence of a first order solid-solid phase transition the wurtzite to rock salt transformation in CdSe nanocrystais Science 265 373... 

J. Klein, E. Kumacheva. Simple liquids confined to molecularly thin layers. I. Confinement-induced liquid-to-solid phase transitions. J Chem Phys 705 6996-7009, 1998. 

Presents temperature-dependent solid-solid phase transition. 

The dependence on the temperature of the specific resistance (Q/cm) of the pure MEPBr and MEMBr complexes, and a 1 1 mixture there of, as obtained in Ref. [73], is listed in Table 4. It is remarkable that within the complex phases consisting of Br2 and either pure MEP or MEM the change of specific resistance at the liquid —> solid phase transition amounts to about one order of magnitude, where as the value is only doubled in the 1 1 mixture. The table also indicates that MEMBr complexes possess higher melting temperatures. 

Figure 4.4 Heat capacity of N as a function of temperature. A solid phase transition occurs at 35.62 K, the melting temperature is 63.15 K, and the normal boiling temperature is 77.33 K.

Experience indicates that the Third Law of Thermodynamics not only predicts that So — 0, but produces a potential to drive a substance to zero entropy at 0 Kelvin. Cooling a gas causes it to successively become more ordered. Phase changes to liquid and solid increase the order. Cooling through equilibrium solid phase transitions invariably results in evolution of heat and a decrease in entropy. A number of solids are disordered at higher temperatures, but the disorder decreases with cooling until perfect order is obtained. Exceptions are... 

In the CO2 phase diagram of Figure 8.1, we considered only (solid + liquid), (vapor + solid) and (vapor + liquid) equilibria. A (solid + solid) phase transition has not been observed in C(>,m but many substances do have one or more. Equilibrium can exist between the different solid phases I, II, III, etc., so that... 

Figure 8.9 is the phase diagram for Sn, a system that shows (solid + solid) phase transitions." Solid II is the form of tin stable at ambient conditions, and it is the shiny, metallic element that we are used to observing. Line ab is the melting line for solid II. Points on this line represent the values of p and T for which... 

In cold climates, metallic tin (solid 11) slowly changes to solid 1. (Solid phase transitions are often slow.) The change from a shiny metallic surface to a brittle and llaky grey surface is known as tin disease. 

In addition to solid phase transitions and the combination of (solid + liquid) with (liquid + liquid) equilibria, solid solutions can form and a variety of... 

Figure 8.23 (Solid + liquid) phase diagram for (. 1CCI4 +. yiCHjCN), an example of a system with large positive deviations from ideal solution behavior. The solid line represents the experimental results and the dashed line is the ideal solution prediction. Solid-phase transitions (represented by horizontal lines) are present in both CCI4 and CH3CN. The CH3CN transition occurs at a temperature lower than the eutectic temperature. It is shown as a dashed line that intersects the ideal CH3CN (solid + liquid) equilibrium line.

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

Einstein heat capacity equation 569-72 Schottky effect 580—5 solid + solid phase transitions 399-404 first-order 402-4 solutes 6... 

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

From the more recent reports cited below, further references to the extensive literature concerned with calcite decomposition may be traced. Other modifications of CaC03 (aragonite and vaterite) undergo solid phase transitions to calcite at temperatures of 728 K and 623—673 K respectively [733], below those of onset of decomposition (>900 K). There is strong evidence [742] that the reaction... 

As with other crystalline substances, on heating coordination compounds may melt, sublime, decompose, or undergo a solid phase transition. The greater complexity of the constituents present increases the number of types of bond redistribution processes which are, in principle, possible within and between the coordination spheres. The following solid-state transitions may be distinguished (i) changes in relative dispositions... 

The heat capacity function for the solid phase Is from Fink (4. Fink points out that although (U,Pu)02 UO2, and ThC>2 have solid-solid phase transitions, the available data (4) make It impossible to determine the existence of a similar phase transition for Pu02 If additional high-temperature measurements indicate the presence of a solid-solid phase transition, the heat capacity of Pu02 between the phase transition and 2701 K may be significantly higher. 

The uncertainties in the condensed-phase thermodynamic functions arise from (1) the possible existence of a solid-solid phase transition in the temperature range 2160 to 2370 K and (2) the uncertainty in the estimated value of the liquid heat capacity which is on the order of 40%. While these uncertainties affect the partial pressures of plutonium oxides by a factor of 10 at 4000 K, they are not limiting because, at that temperature, the total pressure is due essentially entirely to O2 and 0. 

The nonmesogenic compound CB2 is described here, because it shows a reversible distortive solid-solid phase transition at 290.8 K (transition enthalpy 0.9 kj/mol) from the centrosymmetric low temperature phase I to the noncentrosymmetric high temperature phase II. The crystal structures of both solid phases I and II are very similar [45] as demonstrated in Fig. 2. The molecules are arranged in layers. The distances between the cyano groups of adjacent molecules are 3.50 A Ncyano-Ncyano and 3.35 A Ncyano-C ano for phase I and 3.55 A Ncyano-Ncyano and 3.43 A Ncyano-Ccyano for phase II. In the two... 

Allegre CJ, Dupre B, Lewin E (1986) Thorium/uranium ratio of the Earth. Chem Geol 56 217-227 Allegre CJ, Turcotte D (1986) Implications of a two-component marble-cake mantle. Nature 323 123-127 Asimow PD, Hirschmann MM, Ghiorso MS, O Hara MJ Stolper EM (1995) The effect of pressure-induced solid-solid phase transitions on decompression melting of the mantle. Geochim Cosmochim Acta 59 4489-4506... 

N. A. Williams, Y. Lee, G. P. Polli, and T. A. Jennings, The effects of cooling rate on solid phase transitions and associated vial breakage occurring in frozen mannitol solutions, J. Parenter. Sci. Technol., 40,135-141 (1986). 

Miller, M. A. Reinhardt, W. P., Efficient free energy calculations by variationally optimized metric scaling concepts and applications to the volume dependence of cluster free energies and to solid-solid phase transitions, J. Chem. Phys. 2000,113, 7035-7046... 

Fig. 2. Phase diagram for the AlCl -EtMeImCl molten salt ( ) liquid-solid phase transitions and (O) glass transitions. Adapted from Fannin et al. [33] by permission of the American Chemical Society, Inc.

However at elevated temperatures (T2 > Tj, Figure 9) the increased entropy (TAS) associated with an open shell structure overcomes the ti —ti enthalpy of dimerisation associated with these distorted Ti-stacked structures and they undergo a solid-solid phase transition (Figure 9) The high temperature phase is typically associated with a Ti-stack of regularly spaced radicals which exhibit longer inter-radical S- S contacts (ca. 3.7 A). This process was first observed by Oakley60 in the DTA radical thiadiazolopyrazine-l,3,2-dithiazolyl 26, and a number of other derivatives have subsequently been identified which exhibit similar behaviour. These are compiled in Table 1. 

Figure 9 (Top) schematic of bistability in 1,3,2-dithiazolyl radicals arising from a solid-solid phase transition between regular and Peierls distorted n-stacks (bottom) free energy diagram of the two structural phases present...

The sample temperature is increased in a linear fashion, while the property in question is evaluated on a continuous basis. These methods are used to characterize compound purity, polymorphism, solvation, degradation, and excipient compatibility [41], Thermal analysis methods are normally used to monitor endothermic processes (melting, boiling, sublimation, vaporization, desolvation, solid-solid phase transitions, and chemical degradation) as well as exothermic processes (crystallization and oxidative decomposition). Thermal methods can be extremely useful in preformulation studies, since the carefully planned studies can be used to indicate the existence of possible drug-excipient interactions in a prototype formulation [7]. 

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