212
10 Importance of Molecular Crystals
of possible quantum effects. On the other hand, a pair of hydroxy groups can serve as
an Ising-like spin as O·H· · · OH or HO· · · H·O. We already see this type of correlated
dynamics in Sect. 10.1.2. Dimers formed by an H-bond are units of the crystal, and
sit on the center of inversion in the disordered state (above T c = 103 K) [13, 20]. The
symmetry of sitting sites guarantees two states of H-bonding are precisely equivalent
to each other with reversed electric dipole. The bulkiness of the hydrocarbon moiety
[(C 6 H 11 ) 3 C–] forces dimers apart compared with the separation of charges in the
dipole. Crystalline TCHM is, therefore, a physical realization of the DIM. The estimated magnitude of the dipole moment is 7.9 × 10
−30 C m (2.4 D) [20]. Although
the crystal is certainly anisotropic with a triclinic cell, the interdimer distances along
the three crystallographic axes do not differ significantly. The assumption of isotropy
is, therefore, not far from the truth. The system is roughly the system in which Ising
spins are arranged on a lattice of about 10 × 10 × 10 Å
3 .
Experimental temperature dependence of dielectric constant [15] and heat capacity is different from a simple three-dimensional ferro- or antiferroelectrics and
compared favorably with that expected by a highly-anisotropic Ising model [20].
This result is partly consistent with existing reports that the spins exhibit a strong
correlation along the spin axis () [17–19]. The numerical estimates obtained
from the analysis assuming the mean-field model [79, 80] are J /k B ≈ 170 K
and z|J ⊥ |/k B ≈ 1 ∼ 2 K with z being the number of the nearest neighbor spins
(dimers) [20].
Having seen the utility of an isolated H-bonding dimer as an Ising spin with a
significant electric dipole moment, we can imagine its modification concerning its
separation and spatial arrangements. Such modifications will plausibly contribute to
the full clarification of classical DIM.
10.3.4 Exotic Superstructure
As mentioned some times previously, the phase transitions between crystalline phases
have been subject of extensive studies, because they often accompany a drastic change
in material properties of potential applications. The formation of superstructures is
an important class of them. The superstructure is a traditional crystalline structure,
5
the unit cell of which has the size of an integer multiple of the original lattice. The
original lattice is usually stable at the high-temperature side because of its higher
symmetry. Since the relationship between two phases is evident, the formation of
superstructures is one of the best objects of the Landau’s phenomenology of phase
transitions described in Sect. 2.2. It is noteworthy that the low-symmetry phase is
fixed before an assessment on a specific transition starts because the Landau theory
is essentially one for not predicting but understanding.
The theory [1, 81] says that the transition is discontinuous if the third-order
term can survive in the expansion of the thermodynamic potential in terms of the
5 See Sect. 4.2 for the meaning of “traditional.”
10 Importance of Molecular Crystals
of possible quantum effects. On the other hand, a pair of hydroxy groups can serve as
an Ising-like spin as O·H· · · OH or HO· · · H·O. We already see this type of correlated
dynamics in Sect. 10.1.2. Dimers formed by an H-bond are units of the crystal, and
sit on the center of inversion in the disordered state (above T c = 103 K) [13, 20]. The
symmetry of sitting sites guarantees two states of H-bonding are precisely equivalent
to each other with reversed electric dipole. The bulkiness of the hydrocarbon moiety
[(C 6 H 11 ) 3 C–] forces dimers apart compared with the separation of charges in the
dipole. Crystalline TCHM is, therefore, a physical realization of the DIM. The estimated magnitude of the dipole moment is 7.9 × 10
−30 C m (2.4 D) [20]. Although
the crystal is certainly anisotropic with a triclinic cell, the interdimer distances along
the three crystallographic axes do not differ significantly. The assumption of isotropy
is, therefore, not far from the truth. The system is roughly the system in which Ising
spins are arranged on a lattice of about 10 × 10 × 10 Å
3 .
Experimental temperature dependence of dielectric constant [15] and heat capacity is different from a simple three-dimensional ferro- or antiferroelectrics and
compared favorably with that expected by a highly-anisotropic Ising model [20].
This result is partly consistent with existing reports that the spins exhibit a strong
correlation along the spin axis () [17–19]. The numerical estimates obtained
from the analysis assuming the mean-field model [79, 80] are J /k B ≈ 170 K
and z|J ⊥ |/k B ≈ 1 ∼ 2 K with z being the number of the nearest neighbor spins
(dimers) [20].
Having seen the utility of an isolated H-bonding dimer as an Ising spin with a
significant electric dipole moment, we can imagine its modification concerning its
separation and spatial arrangements. Such modifications will plausibly contribute to
the full clarification of classical DIM.
10.3.4 Exotic Superstructure
As mentioned some times previously, the phase transitions between crystalline phases
have been subject of extensive studies, because they often accompany a drastic change
in material properties of potential applications. The formation of superstructures is
an important class of them. The superstructure is a traditional crystalline structure,
5
the unit cell of which has the size of an integer multiple of the original lattice. The
original lattice is usually stable at the high-temperature side because of its higher
symmetry. Since the relationship between two phases is evident, the formation of
superstructures is one of the best objects of the Landau’s phenomenology of phase
transitions described in Sect. 2.2. It is noteworthy that the low-symmetry phase is
fixed before an assessment on a specific transition starts because the Landau theory
is essentially one for not predicting but understanding.
The theory [1, 81] says that the transition is discontinuous if the third-order
term can survive in the expansion of the thermodynamic potential in terms of the
5 See Sect. 4.2 for the meaning of “traditional.”