Molecular crystal global phase diagrams. I. Method of construction

Abstract

A method is described to produce global phase diagrams for single-component molecular crystals with separable internal and external modes. The phase diagrams present the equilibrium crystalline phase as a function of the coefficients of a general intermolecular potential based on rotational symmetry-adapted basis functions. It is assumed that phase transitions are driven by orientational ordering of molecules with a fixed time-averaged shape. The mean-field approximation is utilized and the process begins in a high-temperature disordered reference state, then spontaneous symmetry-breaking phase transitions and phase structure information at lower temperature are sought. The information is mapped onto phase diagrams using the intermolecular expansion coefficients as independent variables. This is illustrated by global phase diagrams for molecules having tetrahedral symmetry (e.g. carbon tetrachloride, adamantane and white phosphorus). Uses of global phase diagrams include crystal structure data mining, guidance for crystal design and enumeration of likely or missing polymorphic structures.

Molecular crystal global phase diagrams. III. Sufficient parameter space determination

“…This kind of hierarchical structure is not incorporated in the GPDs as described by Mettes et al (2004). We find that 60% of crystal structures composed of molecules with T d point-group symmetry are amenable and that eight reference lattices are sufficient to span the observed structures.…”

“…The mathematical details are explained by Mettes et al (2004). They do not use an equation of state and mixing rules but instead rely on fundamental postulates of equilibrium statistical mechanics, a set of basis functions over rotational space SOð3Þ to represent the orientational intermolecular potential, and a set of translational packings over translational space T 3 to represent their translational ordering.…”

In Silico Prediction of Growth and Dissolution Rates for Organic Molecular Crystals: A Multiscale Approach

“…Crystal-like molecules are thereby defined as those having their orientations within a certain threshold value from the orientations of the molecules from the relaxed unit cell used to construct the crystal (called reference orientations) and at least one neighbor among the crystal molecules, as described in detail in our papers [40,51]. However, the identification of an appropriate set of order parameters can be far from trivial in many other cases [107], and a significant number of approaches to differentiate one state from the other can be found in the literature [12,20,33,[96][97][98][108][109][110][111][112][113][114][115][116][117].…”

Molecular crystal global phase diagrams. II. Reference lattices

“…The center-of-mass lattice is used here to be consistent with the reference state employed in the prior work Mettes et al, 2004). Five structures are cubic (also called isometric), one is hexagonal, four are trigonal, eight are tetragonal, six are orthorhombic, 16 are monoclinic and six are triclinic (also called anorthic).…”

“…GPDs also present equilibrium phase behavior, but at least one of the independent variables of the diagram is either a parameter in an empirical equation of state or a parameter in an intermolecular potential. Two independent variables were arbitrarily chosen by Keith et al (2004) and three independent variables were chosen by Mettes et al (2004). Their classification was based on the van der Waals equation of state with simple binary mixing rules.…”