200
10 Importance of Molecular Crystals
identification of systems where the effect of the correlation is significant is currently
of great significance.
It is essential to understand that routine analysis of crystal structure by diffraction, which take only Bragg reflections arising from the long-range periodicity into
account, is insensitive to the correlation at a short distance. A detailed analysis of
diffuse scattering at high angles is necessary because of the short-ranged and intrinsically incoherent nature of the motional correlation [3, 4]. The utilization of the
XAFS (X-ray absorption fine structure) technique, which unveils local structures,
may be useful [5].
10.1.2 Entropic Detection
Concerning the second difficulty in the last section, the enumeration of entropy has a
unique character. Suppose two Ising spins, each of which has two states (↑ and ↓). All
possible states are (↑↑), (↑↓), (↓↑), and (↓↓). If the interaction strongly favors the
same state for interacting spins, the available states are limited to (↑↑) and (↓↓). On
the contrary, the interaction strongly hating the same results in (↑↓) and (↓↑). These
situations share the property that the specification of the state of one spin suffices
the specification of the other. If the interaction extends over n spins, the number of
available states for N spins is not 2
N but 2
N /n .
1 Since the entropy is proportional
to the (natural) logarithm of the number of states, the entropy directly reflects the
presence of strong interaction, which is equivalent to the perfect correlation. Indeed,
the example in Sect. 6.3 is based on the magnitude of entropy of transition. The
drawback of the simple adoption of entropic detection is that it gives no details of the
rate of dynamics. In this respect, the application of the heat capacity spectroscopy
[6] seems promising. The main difficulty exists in its operation frequency, which
is generally low in comparison with the rate of either correlated or uncorrelated
molecular dynamics.
An example of intramolecular motional correlation is the correlated disordering of
ligands in inorganic complexes. Quasi-one-dimensional complexes known as MMX
have a repeat unit shown in Fig. 10.1. Two metal atoms (platinum or nickel) are
bridged by four ligands (RCS
−
2 , R = alkyl group), forming an MM unit. A halogen
(X) bridges two MM units, resulting in an infinite chain of MMX units. The distance
between two sulfur atoms of a bridging CS 2 moiety is longer than the M–M distance. Thus, the two sulfur atoms are not on but slant from the plane defined by the
MMX chain and the carbon atom. Many MMX complexes exhibit a phase transition
between the slant-ordered state and the slant-disordered state. Although the entropy
increments involved in such transitions are well described by the entire disorder in
some complexes [7–9], those of two complexes are significantly smaller than that of
the fully disordered state [10, 11]. In particular, that of Pt 2 (CH 3 CS 2 ) 4 I is comparable
1 We only consider the ferroic case, which favors the same states for interacting spins, to avoid issues
related to the so-called frustration.
10 Importance of Molecular Crystals
identification of systems where the effect of the correlation is significant is currently
of great significance.
It is essential to understand that routine analysis of crystal structure by diffraction, which take only Bragg reflections arising from the long-range periodicity into
account, is insensitive to the correlation at a short distance. A detailed analysis of
diffuse scattering at high angles is necessary because of the short-ranged and intrinsically incoherent nature of the motional correlation [3, 4]. The utilization of the
XAFS (X-ray absorption fine structure) technique, which unveils local structures,
may be useful [5].
10.1.2 Entropic Detection
Concerning the second difficulty in the last section, the enumeration of entropy has a
unique character. Suppose two Ising spins, each of which has two states (↑ and ↓). All
possible states are (↑↑), (↑↓), (↓↑), and (↓↓). If the interaction strongly favors the
same state for interacting spins, the available states are limited to (↑↑) and (↓↓). On
the contrary, the interaction strongly hating the same results in (↑↓) and (↓↑). These
situations share the property that the specification of the state of one spin suffices
the specification of the other. If the interaction extends over n spins, the number of
available states for N spins is not 2
N but 2
N /n .
1 Since the entropy is proportional
to the (natural) logarithm of the number of states, the entropy directly reflects the
presence of strong interaction, which is equivalent to the perfect correlation. Indeed,
the example in Sect. 6.3 is based on the magnitude of entropy of transition. The
drawback of the simple adoption of entropic detection is that it gives no details of the
rate of dynamics. In this respect, the application of the heat capacity spectroscopy
[6] seems promising. The main difficulty exists in its operation frequency, which
is generally low in comparison with the rate of either correlated or uncorrelated
molecular dynamics.
An example of intramolecular motional correlation is the correlated disordering of
ligands in inorganic complexes. Quasi-one-dimensional complexes known as MMX
have a repeat unit shown in Fig. 10.1. Two metal atoms (platinum or nickel) are
bridged by four ligands (RCS
−
2 , R = alkyl group), forming an MM unit. A halogen
(X) bridges two MM units, resulting in an infinite chain of MMX units. The distance
between two sulfur atoms of a bridging CS 2 moiety is longer than the M–M distance. Thus, the two sulfur atoms are not on but slant from the plane defined by the
MMX chain and the carbon atom. Many MMX complexes exhibit a phase transition
between the slant-ordered state and the slant-disordered state. Although the entropy
increments involved in such transitions are well described by the entire disorder in
some complexes [7–9], those of two complexes are significantly smaller than that of
the fully disordered state [10, 11]. In particular, that of Pt 2 (CH 3 CS 2 ) 4 I is comparable
1 We only consider the ferroic case, which favors the same states for interacting spins, to avoid issues
related to the so-called frustration.