Page 38 - Materials Chemistry, Second Edition

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2.3. The Crystalline State

pouring into cold water, a hard, reddish-yellow solid will be formed, comprised of
infinite chains of disordered sulfur atoms (Figure 2.4c). This latter form is known as
catenasulfur, or “plastic sulfur”; however, since it is not thermodynamically stable at
room temperature, it will slowly convert back to the powdery S 8 form. The other
Group 16 congeners also possess this structural diversity, with the relative thermody-
namic stability of a particular allotrope being governed by the structure with the
lowest overall free energy.
If the chemical contents of a polymorph are different than other forms, it is
designated as a pseudopolymorph. [7] This often occurs due to the presence of
differing amounts of solvent (e.g., clathrates, host-guest, or inclusion compounds),
which will alter physical properties of the crystals such as melting points and
solubilities. Polymorphism and pseudopolymorphism may be observed when differ-
ent experimental conditions are used for synthesis. For example, if crystals are
grown by sublimation, changing the temperature will often yield different crystal
structures, possibly even metastable phases that are kinetically favored.
When different compounds yield almost identical crystals, the forms are referred
to as isomorphs. The word “almost” is indicated here, as isomorphs are not exactly
the same. Although the arrangement of atoms/ions in the lattices are identical, one
or more of the atoms in the lattice have been replaced with another component. For
example, alums of the general formula (M) 2 (SO 4 ) · (M) 2 (SO 4 ) 3 · 24H 2 O may
crystallize as isomorphs where one of the monovalent or trivalent metals is sub-
stituted with another.
The conversion between polymorphs may be observed by differential scanning
calorimetry (DSC), which shows peaks corresponding to endothermic (melting) or
exothermic ((re)crystallization) events associated with structural changes. Figure 2.5
shows the differential scanning calorimetry (DSC) curves of two polymorphs
(designated as I R and II o ) of picryltoluidine, obtained via crystallization from
different solvents. Whereas form I R exhibits an endothermic melting peak at

166 C, form II o melts at 163 C. Further, the enthalpies of fusion for I R and II o
forms are 31.3 kJ/mol and 28.6 kJ/mol, respectively. The heat of fusion rule states
that if the higher melting form has the lower enthalpy of fusion, the two forms are
enantiotropic (i.e., two forms have differing stabilities at specific temperature
ranges). On the other hand, if the lower melting form has the lower enthalpy of
fusion (as exhibited here), the two forms are monotropic (i.e., one form is more
stable at all temperatures). [8]
The rate of a polymorphic phase transition depends on nucleation and growth
processes, which are related to the mobility of atoms/molecules in the solid state.
The Avrami equation (Eq. 7) may be applied to describe the degree of transforma-
tion, X, as a function of time, t:

n
kt
ð7Þ XðtÞ¼ 1 e ;
where n and k are constants related to the relative importance of nucleation and
growth, respectively. [9]