Enthalpies of Phase Transformations

Calorimetry of non-reacting systems involves the measurement of heat capacity dependencies on temperature, which enables us to calculate the enthalpies of phase transformations. Based on the prevailing mode of the heat exchange between their individual parts, calorimeters for this purpose can be classified as low-, medium-, and high-temperature calorimeters. In the measurement of thermodynamic parameters of molten electrolytes, mostly the last two types of calorimeters are used. 

The standard entropy of a-SnSe was evaluated to be 86.93 J-K" -mol , corresponding to Af5° (SnSe, a, 298.15 K) = - 6.3 J-K -mor, in the thermodynamic optimisation and assessment of the Sn-Se system in [96FEU/MAJ]. The value originates mainly from the modelling and assumptions made about the liquid phase in the system and the recalculation to 298.15 K by the use of enthalpies of phase transformations and heat capacities. The only experimental determination of the entropy at low temperatures was made by Melekh, Stepanova, Fomina, and Semenkovich [71MEL/STE] who performed emf measurements on the galvanic cells... 

Schick s work includes the study of borides, carbides, nitrides, and oxides of some elements in Groups IIA, IIIB, IVA, IVB, VB, VIIB, and VIII as well as selected rare earths and actinides. As far as possible, the tables have been made compatible with the JANAF tables. Among the subjects treated are phase diagrams, heat capacities, enthalpies, entropies, enthalpies of phase transformation, formation, and reaction, melting temperatures, triple points, free energies of formation, vapour pressures, compositions of vapour species, ionization and appearance potentials, e.m.f. of cells, and enthalpies of solution and dilution. Volume 1 summarizes the techniques used to analyse data and cites the data analysed, and Volume 2 gives tables of values produced by this study. 

Several papers report [4] that liquid alumina solidifies not in the thermodynamically most stable phase of (X-AI2O3, but rather in the form of Y-AI2O3. This is attributed to the fact that the solidified phase structure is basically determined by the relative critical free enthalpies of nucleation of alternative crystal structures. Consequently, not surprising, that considerable part of spheroidized particles composed of y-AbOs and other metastable phases (such as 8, 0) of alumina (Fig. 7). The latter were formed from the y phase according to the usual route of phase transformation on cal-... 

The enthalpy change of phase transformation can be directly measured from the corresponding peak area of a DSC curve. The DSC is commonly plotted as per mass unit versus temperature. The total enthalpy change AH should be proportional to the peak area (Ap). 

Enthalpies of phase transitions (fusion, solid-solid transformation, sublimation, and solution)... 

However, the difference A /z -A /z represents the enthalpy A /z° accompanying the phase change of the component in question between P and P . Similarly, the difference A 5°-A 5 represents the opposite of entropy associated with the same transformation. The slope of the straight line PP is therefore given by the opposite of the ratio of the enthalpy of phase change of the compound involved to the corresponding entropy ... 

Figure 2. The enthalpy, AH, of the phase transformation can be calculated from the variation of In P laleai] with reciprocical temperature in a van t Hoff plot.

The solid product, BaO, was apparently amorphous and porous. Decomposition rate measurements were made between the phase transformation at 1422 K and 1550 K (the salt melts at 1620 K). The enthalpy and entropy of activation at 1500 K (575 13 kJ mole-1 and 200 8 J K"1 mole-1) are very similar to the standard enthalpy and entropy of decomposition at the same temperature (588 7 kJ and 257 5 J K-1, respectively, referred to 1 mole of BaS04). The simplest mechanistic explanation of the observations is that all steps in the reaction are in equilibrium except for desorption of the gaseous products, S02 and 02. Desorption occurs over an area equivalent to about 1.4% of the total exposed crystal surface. Other possible models are discussed. 

When the free enthalpy of reaction AG for the transformation of the structure of a compound to any other structure is positive, then this structure is thermodynamically stable. Since AG depends on the transition enthalpy AH and the transition entropy AS, and AH and AS in turn depend on pressure and temperature, a structure can be stable only within a certain range of pressures and temperatures. By variation of the pressure and/or the temperature, AG will eventually become negative relative to some other structure and a phase transition will occur. This may be a phase transition from a solid to another solid modification, or it may be a transition to another aggregate state. 

MnAs exhibits this behavior. It has the NiAs structure at temperatures exceeding 125 °C. When cooled, a second-order phase transition takes place at 125 °C, resulting in the MnP type (cf. Fig. 18.4, p. 218). This is a normal behavior, as shown by many other substances. Unusual, however, is the reappearance of the higher symmetrical NiAs structure at lower temperatures after a second phase transition has taken place at 45 °C. This second transformation is of first order, with a discontinuous volume change AV and with enthalpy of transformation AH. In addition, a reorientation of the electronic spins occurs from a low-spin to a high-spin state. The high-spin structure (< 45°C) is ferromagnetic,... 

An enormous number of phase transitions are known to occur in common solid compounds. For example, silver nitrate undergoes a displacive phase transition from an orthorhombic form to a hexagonal form at a temperature of approximately 162°C that has a enthalpy of 1.85 kj/mol. In many cases, the nature of these transitions are known, but in other cases there is some uncertainty. Moreover, there is frequently disagreement among the values reported for the transition temperatures and enthalpies. Even fewer phase transitions have been studied from the standpoint of kinetics, although it is known that a large number of these transformations follow an Avrami rate law. There is another complicating feature of phase transitions that we will now consider. 

Although there are other ways, one of the most convenient and rapid ways to measure AH is by differential scanning calorimetry. When the temperature is reached at which a phase transition occurs, heat is absorbed, so more heat must flow to the sample in order to keep the temperature equal to that of the reference. This produces a peak in the endothermic direction. If the transition is readily reversible, cooling the sample will result in heat being liberated as the sample is transformed into the original phase, and a peak in the exothermic direction will be observed. The area of the peak is proportional to the enthalpy change for transformation of the sample into the new phase. Before the sample is completely transformed into the new phase, the fraction transformed at a specific temperature can be determined by comparing the partial peak area up to that temperature to the total area. That fraction, a, determined as a function of temperature can be used as the variable for kinetic analysis of the transformation. 

Determination of transformation enthalpies in binary systems. Just as consistent values of for elements can be obtained by back-extrapolation from binary systems, so it is possible to obtain values of by extrapolating the enthalpy of mixing vs composition in an alloy system where the phase has a reasonable range of existence. The archetypal use of this technique was the derivation of the lattice stability of f.c.c. Cr from the measured thermodynamic properties of the Ni-based f c.c. solid solution (7) in the Ni-Cr system (Kaufman 1972). If it is assumed that the f.c.c. phase is a regular solution, the following expression can be obtained ... 

---