Ru lattice energy free#
The relative free energy determines which polymorph should be favourable under given thermodynamic conditions. For these reasons, there is a strong motivation to develop our fundamental understanding of polymorphism, of property differences between polymorphs and, ultimately, the ability to predict possible polymorphs a priori. 3 Unexpected polymorphism can have far-reaching economic and medical, 4,5 as well as legal 6 consequences. 1 Introduction Polymorphism, the possibility of a compound to exist in at least two different crystalline phases, 1 has important implications for the development of pharmaceuticals, organic semiconductors, 2 explosives and any other material where solid state properties must be controlled.
However, these relatively small vibrational free energy contributions are large enough to cause a re-ranking of polymorph stability below, or at, room temperature in 9% of the polymorph pairs. The distribution of vibrational energy differences is narrower than lattice energy differences, rarely exceeding 2 kJ mol −1. Unsurprisingly, vibrational contributions to polymorph free energy differences at ambient conditions are dominated by entropy differences. Polymorphic lattice energy differences are typically very small: over half of polymorph pairs are separated by less than 2 kJ mol −1 and lattice energy differences exceed 7.2 kJ mol −1 in only 5% of cases. Distributions of the differences in lattice energy, free energy, zero point energy, entropy and heat capacity between polymorphs are presented.
Rigid molecule lattice dynamical calculations have also been performed to estimate the vibrational contributions to lattice free energies. A computational study of 1061 experimentally determined crystal structures of 508 polymorphic organic molecules has been performed with state-of-the-art lattice energy minimisation methods, using a hybrid method that combines density functional theory intramolecular energies with an anisotropic atom–atom intermolecular model.
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