Polymorphic transformation, enthalpy

For many years, it was thought, purely on an empirical basis, that if the enthalpy change for a given reaction were negative, that is, if heat were evolved at constant pressure, the transformation could occur spontaneously. This rule was verified for many reactions. Nevertheless, numerous exceptions, exist such as the polymorphic transformation of a quartz to (3 quartz at 848 K and atmospheric pressure ... 

The adopted enthalpies of the polymorphic transformation and fusion of NaOH are mean values from the work of Douglas and Dever (9), Popov and Ginzburg (IJ ) and Reshetnikov and Baranskaya ( ). T,. j.g - d are from Reshetnikov and Baranskaya (12). 

Mitsuhashi T, Kleppa OJ (1979) Transformation enthalpies of the Ti02 polymorphs. J Am Ceram Soc 62 356-357... 

Enthalpy of polymorphic transformation is the heat connected with the transition of the compound from one crystallographic modification to the other. 

The transition temperatures and enthalpies of the various polymorphic transformations of ln2Se3(cr) are discussed in detail in the reviews in [93CHA] and [98VAS/DAO]. The values recommended in the two reviews are similar and those in [98VAS/DAO] are ... 

Table 1 Surface enthalpies and transformation enthalpies relative to bulk stable polymorph for oxides (adapted from Navrotsky [94])...

Solids absorb heat on melting and, with the notable exception of ice, expand. They evolve heat when they undergo polymorphic transformation to a more stable polymorphic and contract. Consequently, dilatometric (specific volume-temperature) curves bear a close resemblance to calorimetric (enthalpy-temperature) curves. The melting dilation corresponds to the heat of fusion, and the coefficient of cubical expansion, a, corresponds to the specific heat capacity, c. The ratio cja is virtually a constant independent of temperature. 

Whilst sublimation and melting are tirst-order phase transitions with a change of both the structure and the aggregate state, polymorphic transformations in crystals change structures within the same aggregate state. Therefore the enthalpy of such transitions (AHtr) is much smaller than AHg and is comparable with AHm- Values of AHtt for a number of elemental solids and compounds are given in Tables 9.9 and 9.10, respectively. 

Table 9.10 Enthalpies of polymorphic transformations, AH (kJ/mol) in selected compounds...

Transition pressures were determined by equating enthalpies of different polymorphs via the common tangent construction. We found that ratile transforms to columbite structure at 11.8 GPa with a small volume change of 3%. These results agree well with experimental... 

Since the heat absorbed or released by a system at constant pressure is equal to its change in enthalpy, enthalpy is often called heat content. If a phase transformation (i.e. melting or transformation to another solid polymorph) takes place within... 

If a substance undergoes a transformation from one physical stale to another, such as a polymorphic transition, the fusion or sublimation of a solid, or the vaporization of a liquid, the heat adsorbed hy the substance during the transformation is defined as the latent heat of transformation (transition, fusion, sublimation or vaporization). It is equal in the enthalpy change of the process, which is the difference between the enthalpy of the substance in the two states at (he temperature of the transformation. For the purpose of thcrmochemical calculations, i( is usually reported as a molar quantity with die units of calories (or kilocalories) per mule (or gram formula weight). The symbol L or AH. with a subscript i.f (or in), s. and n is commonly used and the value is usually given at the equilibrium temperature of the transformation under atmospheric pressure, or at 25 C. 

Fig. 9.2. Flowchart of prilocaine hydrochloride solid state forms and melt with transformation temperatures under ambient pressure conditions (left) and semi-schematic energy/temperature diagram of the polymorphs (right). Key H, enthalpy G, Gibbs free energy AHf, heat of fusion Liq, liquid phase (melt). Reproduced from [36]...

Navrotsky A, Kleppa OJ (1967) Enthalpy of the anatase-rutile transformation. J Am Ceram Soc 50 626 Navrotsky A, Jamieson JC, Kleppa OJ (1967) Enthalpy of transformation of a high-pressure polymorph of titanium dioxide to the ratile modification. Science 158 388-389 Navrotsky A, Petrovic 1, Hu Y, Chen CY, Davis ME (1995) Little energetic limitation to microporous and mesoporous materials. Microporous Mater 4 95-98... 

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